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- 1. Bargaining Behaviour at the Grand Bazaar of Istanbul Bachelor’s Thesis supervised by the Department of Economics at the University of Zurich Prof. Dr. María Sáez Martí to obtain the degree of Bachelor of Arts UZH (in Economics) Author: Batuhan Kalyoncu Course of Studies: Economics Student ID: 10-918-936 Address: Gubelstrasse 44 8050 Zurich E-Mail: batuhan.kalyoncu@uzh.ch Closing date: May 19, 2016
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- 3. Abstract T his thesis analyses the bargaining behaviour at the Grand Bazaar of Istanbul. This study examines how real-life bargaining processes can be modelled using game theoretic approaches with focus on bargaining powers and reservation values. First, basic concepts of game theory are introduced and negotiation processes are described, followed by multiple possible modiﬁcations of bargaining games. Finally results of an on site ﬁeld research are presented and their meaning for the bargaining models are explained. These results give insights into how some buyers’ characteristics affect sellers’ price settings and how potential customers can avoid inﬂated prices. iii
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- 5. Acknowledgments F irst and foremost, I want to thank my supervisor Prof. Dr. María Sáez Martí for introducing me to the fascinating world of game theory and for her continuous feedback and support. Additionally, I want to thank Numan Hocao˘glu, member of the Istanbul chamber of commerce, and his son Selman, for introducing me to the right people at the Grand Bazaar. It would have been impossible to conduct my survey without them. Specially I want to mention the ongoing support of my parents, Leyla Görpe and Ibrahim Kalyoncu, and my manager at work Laura Ameti, without whom my studies at the University of Zurich would not have been possible. I am especially grateful for my girlfriend Seher Ilciktay’s and Daniel Dürr’s support and motivation in times of doubt. Additionally, I want to thank Christian Rösch and Tim Naef for proofreading and giving my thesis the ﬁnal touch. Last but not least, I want to thank Sebastian Pinegger and Janosh Köfferli for their support and feedback during the evaluation and implication of the collected data. v
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- 7. Contents Abstract iii Acknowledgments v 1 Introduction 1 2 Extensive-Form Games 3 2.1 Game Trees . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Games with Imperfect Information . . . . . . . . . . . . . . . 6 2.3 Extensive-Form Games in Strategic-Form . . . . . . . . . . . 7 3 Dominance, Best Response and Nash Equilibrium 9 3.1 Dominance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.2 Best Response . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.3 Nash Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . 12 4 Equilibrium Reﬁnements 15 4.1 Backward Induction . . . . . . . . . . . . . . . . . . . . . . . 15 4.2 Subgame Perfect Equilibrium . . . . . . . . . . . . . . . . . . 16 5 Games with Incomplete Information 19 5.1 Belief, Knowledge and Sequential Equilibrium . . . . . . . . . . . . . . . . . . . . . . 20 5.2 Bayesian Nash Equilibrium . . . . . . . . . . . . . . . . . . . 22 vii
- 8. viii CONTENTS 6 Cooperative Bargaining 25 6.1 The model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 6.2 Nash Bargaining . . . . . . . . . . . . . . . . . . . . . . . . . 27 6.2.1 Nash Axioms . . . . . . . . . . . . . . . . . . . . . . . 27 6.2.2 The Nash Bargaining Solution . . . . . . . . . . . . . 28 7 Noncooperative Bargaining 31 7.1 Ultimatum Games . . . . . . . . . . . . . . . . . . . . . . . . 31 7.2 Rubinstein’s Basic Alternating-Offers Model . . . . . . . . . 33 7.3 Asymmetric Information . . . . . . . . . . . . . . . . . . . . . 36 7.3.1 One-Sided Uncertainty . . . . . . . . . . . . . . . . . . 37 7.3.2 Two-Sided Uncertainty . . . . . . . . . . . . . . . . . 39 7.4 Other Modiﬁcations . . . . . . . . . . . . . . . . . . . . . . . 40 7.4.1 Risk of Breakdown . . . . . . . . . . . . . . . . . . . . 40 7.4.2 Outside Options . . . . . . . . . . . . . . . . . . . . . 40 7.4.3 Inside Options . . . . . . . . . . . . . . . . . . . . . . 41 7.5 Reputation Effects . . . . . . . . . . . . . . . . . . . . . . . . . 41 8 The Grand Bazaar of Istanbul 43 8.1 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 8.2 Merchants at the Grand Bazaar . . . . . . . . . . . . . . . . . 46 9 The Field Research 47 9.1 Questionnaire and Conduction . . . . . . . . . . . . . . . . . 47 9.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 9.3 Implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 10 Conclusion 65 References 67 Appendices 69 A Survey 71
- 9. CONTENTS ix B Data Analysis 75 B.1 Histograms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 B.2 Boxplots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 C R-Code Snippets 85 C.1 Histograms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 C.2 Boxplots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 D Statutory Declaration 87
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- 11. List of Figures 1 First decision . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 Adding the seller . . . . . . . . . . . . . . . . . . . . . . . . . 6 3 Imperfect information . . . . . . . . . . . . . . . . . . . . . . 7 4 The strategic-form of Figure 3 . . . . . . . . . . . . . . . . . . 7 5 The strategic-form of Figure 2 . . . . . . . . . . . . . . . . . . 8 6 Go in dominates Stay out . . . . . . . . . . . . . . . . . . . . 10 7 Go in dominates Stay out again . . . . . . . . . . . . . . . . . 11 8 The strategic-form of Figure 7 . . . . . . . . . . . . . . . . . . 11 9 Tea or Coffee . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 10 Non-credible Nash equilibrium . . . . . . . . . . . . . . . . . 17 11 Subgame perfect Nash equilibrium . . . . . . . . . . . . . . . 18 12 Sequential rationality . . . . . . . . . . . . . . . . . . . . . . . 21 13 Strategic-form of Figure 12 . . . . . . . . . . . . . . . . . . . 21 14 Conditional probabilities . . . . . . . . . . . . . . . . . . . . . 24 15 The Nash bargaining solution . . . . . . . . . . . . . . . . . . 29 16 The Nash bargaining solution in a simple way . . . . . . . . 30 17 Ultimatum game . . . . . . . . . . . . . . . . . . . . . . . . . 32 18 A two-period game . . . . . . . . . . . . . . . . . . . . . . . . 35 19 Life at the Grand Bazaar in the 19th century . . . . . . . . . 45 20 The Grand Bazaar today . . . . . . . . . . . . . . . . . . . . . 64 xi
- 12. xii LIST OF FIGURES 21 1st level histogram . . . . . . . . . . . . . . . . . . . . . . . . 75 22 2nd level histogram clustered to items . . . . . . . . . . . . . 76 23 2nd level histogram clustered to property . . . . . . . . . . . 77 24 3rd level histogram clustered to professions and property (1) 78 25 3rd level histogram clustered to professions and property (2) 79 26 3rd level histogram clustered to professions and property (3) 80 27 3rd level histogram clustered to professions and property (4) 81 28 Boxplots of 1st&2nd level data (1) . . . . . . . . . . . . . . . . 82 (a) Age . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 (b) Nationality . . . . . . . . . . . . . . . . . . . . . . . . . 82 (c) Gender . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 (d) Interest in product . . . . . . . . . . . . . . . . . . . . . 82 (e) Wearing apparel . . . . . . . . . . . . . . . . . . . . . . 82 (f) Accent . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 29 Boxplots of 1st&2nd level data (2) . . . . . . . . . . . . . . . . 83 (a) Sympathy . . . . . . . . . . . . . . . . . . . . . . . . . . 83 (b) Number of articles . . . . . . . . . . . . . . . . . . . . . 83 (c) Time of the day . . . . . . . . . . . . . . . . . . . . . . . 83 (d) Date . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 (e) Wanting a receipt . . . . . . . . . . . . . . . . . . . . . . 83 (f) Paying in cash . . . . . . . . . . . . . . . . . . . . . . . 83
- 13. List of Tables 1 Size of clusters . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 2 Mean and standard deviation of the characteristics . . . . . 52 3 Correlation Matrix . . . . . . . . . . . . . . . . . . . . . . . . 58 4 Price range distribution . . . . . . . . . . . . . . . . . . . . . 59 5 Discount distribution . . . . . . . . . . . . . . . . . . . . . . . 59 xiii
- 14. xiv LIST OF TABLES
- 15. Chapter 1 Introduction M ost of the tourists in Turkey probably know that negotiation at a bazaar is totally normal. It is one of the biggest and most important parts of a merchant’s job and his ability of negotiation can determine how big his revenue will be at the end of the day. Therefore, how should a tourist who is visiting the Grand Bazaar of Istanbul prepare for shopping? He1 could simply go to a store in the Bazaar and ask for a price, then negotiate until a price is reached which he thinks is fair based on some exogenous beliefs about the product’s value. The tourist would probably be better off trying to predict the prices from some knowledge about the industry. In particular, a tourist could do some research and ﬁnd out how much it costs to produce a product. He could invest some time in bargaining with different vendors for similar products to gain more information. He could also try to hide some of his characteristics. For instance, a very wealthy tourist would be advised to leave his Rolex in the hotel safe to achieve a better bargaining outcome. This thesis has two goals, one is to ﬁnd out whether or not a real-life bargaining situation at the Grand Bazaar can be modelled with a game theoretic approach and the other is how certain buyers’ characteristics might inﬂuence sellers’ price settings and therefore the bargaining outcome. Firstly, chapter 2 will introduce the concept of game trees. They are a 1For simplicity and in order to avoid gender discrimination, the players in the games will be masculine throughout the thesis. 1
- 16. 2 CHAPTER 1. INTRODUCTION common way to describe a game with multiple rounds and two players. A game displayed with a game tree is called an extensive-form game. In chapter 3, the focus will lie on the negotiators’ strategies and how some may outperform the others, followed by an introduction to the concept of the Nash equilibrium. Chapter 4 will illustrate how a Nash equilibrium can be found using backward induction. This concept is commonly used to analyse extensive-form games in detail. It should be noted that not all the Nash equilibria are reasonable in continuous games. For instance, if a tourist threatens a seller that he will buy the same good at his competitor (who happens to be more expensive) unless he gives him a discount of 20%, this would be an "empty threat". Strategies like that would not be optimal to carry out. To rule out such strategies, Selten (1965) introduced his concept of subgame perfection. In chapter 5, the attention will be focussed to games with imperfect information, where players are unsure about their opponents’ payoffs. Regarding the initial situation at a bazaar, this will be more realistic. In chapter 6, the model of cooperative bargaining games will be dis- cussed, introducing the Nash bargaining model and its axioms to build the foundation for the non-cooperative bargaining games. In chapter 7 an ultimatum game will be analysed followed by a closer look at the Rubinstein’s alternating-offers model. It will be showed how equilibria in a model with asymmetric information depend on bargaining power and how this power is affected by reputation effects. After learning more about some basic bargaining models, it will be interesting to observe how these models work in a real-life situation. There are just a few places on earth like the Grand Bazaar of Istanbul where bargaining has such a long-standing tradition. Chapter 8 will contain some background infor- mation about the Grand Bazaar’s history and provide some insights on the sellers’ mentality and the Turkish culture. In Chapter 9, the conducted ﬁeld research at the Grand Bazaar will be explained and presented. This thesis will be concluded by the discussion of how buyers’ attributes affect the price settings of sellers and what a tourist should pay attention to before shopping at the Grand Bazaar.
- 17. Chapter 2 Extensive-Form Games I n this chapter, a graphical way of describing games will be introduced. Games in this form are called extensive-form games. A game in extensive form depicts the rules of the game, the order in which the players take action, all the information available when it is their move and the payoffs at any terminal point. An extensive-form game is portrayed by a game tree and its starting point is called the root. All the outgoing edges from the root end in vertices which represent different positions in the game. Vertices without outgoing edges are terminal positions where the game ends, also called the leaves. Every terminal vertex has a payoff for each player deﬁning their outcomes if the game ends at this position. Non-terminal vertices represent either a move by "Nature"1 or a position in the game where one of the players needs to move. There are always probability distributions at every Nature-move vertex for every possible track emerging from it. In a game with imperfect information, players do not necessarily know their position. If a player could be at more than one vertex, given the information he has at this stage of the game, the combination of all vertices he could be positioned at is called an information set.2 On the contrary, in a game with perfect information, every player always knows his position and 1e.g. a toss of a coin or a die 2e.g. blackjack; one card is always hidden from the players, therefore it is impossible for them to know at which point in a game they are located at. 3
- 18. 4 CHAPTER 2. EXTENSIVE-FORM GAMES every move which had led to it when he is called to take action. A player’s strategy is any action he could choose at any information set and it will determine his action at any stage of the game. In a game with no moves by Nature, the strategies of the players determine a path from the root to a leaf which is called the play of a game. If there are moves by Nature there will be several plays with corresponding probability distributions over the possible outcomes of the game. (Maschler, Solan, & Zamir, 2013, p. 39-42) Even if the players have different information at various locations at the game, it is crucial that they have a shared understanding of the game as a whole. They need to know how the game looks and that at some point in the game some players may not be able to distinguish between nodes in the same information set. This shared understanding of the game is called common knowledge and is deﬁned as follows: Deﬁnition 1 [COMMON KNOWLEDGE]: A particular fact F is said to be common knowledge between the players if each player knows F, each player knows that the others know F, each player knows that every other player knows that each player knows F, and so on. (Watson, 2013, p. 44) 2.1 Game Trees Imagine a tourist must decide between going to the Grand Bazaar and staying at his hotel room. This decision tree would look like the one in Figure 1. The upper node is the start of the game and is thereby the initial node where the tourist needs to decide whether to stay or leave. Every extensive-form game always has only one initial node. The tourist has only two possible strategies: STourist = {Stay, Leave}. This is a convention where all possible strategies are written as a vector. If the tourist decides to go to the Grand Bazaar, he will walk past a lot of shops where sellers need to decide between waiting for the tourist to enter and trying to lure him in. The tourist then can decide whether to go in or not. Figure 2 shows how the decision tree expands with the
- 19. 2.1. GAME TREES 5 Tourist Stay Leave Figure 1: First decision added possibilities of choices. Additionally, there are now payoffs under every node without outgoing branches. Those are terminal nodes and their payoffs determine the order of preference for each player. The payoffs or utilities in economic games are often about monetary rewards. In this example, the utilities are simply transformed into made up numbers. It will be pretended that every store in the Grand Bazaar has something interesting in it and ﬁnding it brings a payoff of 10 to a tourist. On the contrary, leaving his hotel room costs him 5, because it is an effort to get out of a comfortable hotel bed. Additionally, the tourist in this example loves attention and therefore likes it when sellers approach him. This increases his output by 5. However, to lure a tourist in is hard work for a seller and costs him 5, whereas a tourist coming into his store gives him a payoff of 10. In the example of Figure 2, it can be stated that if the tourist leaves his hotel room and the seller waits for the tourist to come in, who actually then enters the shop, by following the branches it can be observed that the tourist will get a payoff of 5 and the seller a payoff of 10. It is a common convention that the ﬁrst number is the ﬁrst player’s payoff, in this example the tourist. Note that a differentiation is needed between the two Go in’s and the two Stay out’s. An apostrophe has been introduced to do so. This way it is possible to just name a player and an action to deﬁne where exactly in the tree it is referred to. The tourist now has 8 different strategies: STourist ={(Stay, Go in, Go in’), (Stay, Go in, Stay out’), , (Stay, Stay Out, Go in’), (Stay, Stay out, Stay out’), (Leave, Go in, Go in’), (Leave, Go in, Stay out’), (Leave, Stay out, Go in’), (Leave, Stay out, Stay out’)}, while the seller has two: SSeller ={Wait, Lure}. (Watson, 2013, p. 10-13)
- 20. 6 CHAPTER 2. EXTENSIVE-FORM GAMES Tourist (0, 0) Stay Seller Tourist (5, 10) Go in (−5, 0) Stay out Wait Tourist (10, 5) Go in’ (0, −5) Stay out’ Lure Leave Figure 2: Adding the seller 2.2 Games with Imperfect Information Whereas in games similiar to the one in Figure 2, where every player exactly knows at which vertex in the game tree the game is currently at, in most games this is not the case. Games in which a player does not have perfect knowledge of actions prior to that stage of the game are called games with imperfect information. In Figure 3, the seller does not know if the tourist is eager to buy or not. He needs to decide whether he offers the tourist a high or low price for certain goods. The ellipse surrounding the seller’s two vertices represents the fact that when it is his turn to take action, he does not know on which vertex he currently is. In this game both players only have two strategies: STourist ={Eager to buy, Not}, SSeller ={High, Low} (Maschler et al., 2013, p. 52)
- 21. 2.3. EXTENSIVE-FORM GAMES IN STRATEGIC-FORM 7 Tourist (0, 10) High (5, 5) Low Eager to buy (0, 0) High (5, 5) Low Not Seller Figure 3: Imperfect information Seller Tourist Eager to buy Not High (0,10) (0,0) Low (5,5) (5,5) Figure 4: The strategic-form of Figure 3 2.3 Extensive-Form Games in Strategic-Form It is possible to draw all extensive-form games in strategic-form. The strategic-form is described by matrices and looks like Figure 4. The different players and their strategies are outside of the matrix and the different payoffs are inside. If a path to a terminal point is followed, for instance, the path on the left hand side (Eager to buy & High), the payoff at that leaf can be compared to the one in the matrix where row "High" intercepts with column "Eager to buy". It is very important to depict every single strategy of all the players when drawing a game tree to its strategic-form. For example, transforming Figure 2 in its strategic-form would look like Figure 5, where S stands for "Stay", G for "Go in", L for "Leave" and SO for "Stay out". It is easier to ﬁnd some properties like dominance and Nash equilibria by using the strategic-form. Those properties will be elaborated in the next chapter.
- 22. 8 CHAPTER 2. EXTENSIVE-FORM GAMES Tourist Seller Wait Lure (S,G,G’) (0,0) (0,0) (S,G,SO’) (0,0) (0,0) (S,SO,G’) (0,0) (0,0) (S,SO,SO’) (0,0) (0,0) (L,G,G’) (5,10) (10,5) (L,G,SO’) (5,10) (0,-5) (L,SO,G’) (-5,0) (10,5) (L,SO,SO’) (-5,0) (0,-5) Figure 5: The strategic-form of Figure 2
- 23. Chapter 3 Dominance, Best Response and Nash Equilibrium T his chapter introduces three of the most important concepts of game theory. They are the foundation of most theories of rational behaviour1 and crucial for ﬁnding ideal strategies. A game has always three elements: the set of players i ∈ I, which will always be a ﬁnite set {1, 2, ...I} regarding a situation at a bazaar, the pure-strategy space Si for each player i, and the payoff functions ui(s) for each proﬁle s = (s1, ..., sI) of strategies. Pure strategy means that a player will choose one strategy certainly or with p = 1. Any time p = {0, 1} it is referred to a mixed strategy σ. If a player chooses action A and B randomly with p between 0 and 1, the numbers p and 1 − p constitute a probability distribution over the set {A, B}. Whenever it is referred to all players except player i, they will be denoted by "−i". (Fudenberg and Tirole, (1991), p. 4; Watson, (2013), p. 37) 1Each player chooses the strategy which leads to the outcome he prefers the most. Classic game theory assumes that players are perfect calculators and make no mistakes following their best strategy. 9
- 24. 10 CHAPTER 3. DOMINANCE, BEST RESPONSE & NE Tourist (5, 10) Go in (−5, 0) Stay out Figure 6: Go in dominates Stay out 3.1 Dominance The bottom part of the left hand side of Figure 2 will be used to explain dominance. It is perfectly clear that, when it is the tourist’s turn to take action at the root shown in Figure 6, he will always decide to go in. The same applies to the decision node at the same level on the right hand side of Figure 2. In a game like shown in Figure 7, where seller and tourist basically choose their strategies at the same time, strategy "Go in" has an interesting property. Regardless of the seller’s strategy, "Go in" always results in a higher payoff than "Stay out". In cases like these, where one strategy is always better independent of other players’ strategies, technically it is stated that "Stay out" is strictly dominated by "Go in", and thus "Stay out" should never be played by a rational player. Note that the seller also has a dominated strategy. If the tourist decides to go in, he should wait and if the tourist decides to stay out, he should wait again. This means that strategy "Lure" is strictly dominated by "Wait". Deﬁnition 2 [DOMINANCE]: A pure strategy si of player i is dominated if there is a strategy (pure or mixed) σ ∈ ∆Si such that ui(σi, s−i) > ui(si, s−i), for all strategy proﬁles s−i ∈ S−i of the other players. (Watson, 2013, p. 49-50) For Dominance there must be a strict inequality in the equation, but there is a version which needs to be considered based on a weaker condition.
- 25. 3.1. DOMINANCE 11 Seller (10, 5) Go in (0, −5) Stay out Wait (5, 10) Go in (−5, 0) Stay out Lure Tourist Figure 7: Go in dominates Stay out again Deﬁnition 3 [WEAKLY DOMINATED]: The strategy si is weakly domi- nated if there exists a σi such that the inequality in Deﬁnition 1 holds with weak inequality, and the inequality is strict for at least one s−i. (Maschler et al., 2013, p. 90) It gets even clearer by using the strategic-form of Figure 7. You can compare the seller’s payoffs in the top row with the corresponding payoffs in the bottom row. The same is possible with the tourist’s columns. Usually dominated rows and columns are crossed out, since they do not have to be considered any longer for the rest of the game. Eliminating them may reveal new dominated strategies. Seller Tourist Go in Stay out Wait (10,5) (0,-5) Lure (5,10) (-5,0) Figure 8: The strategic-form of Figure 7
- 26. 12 CHAPTER 3. DOMINANCE, BEST RESPONSE & NE 3.2 Best Response Many games do not have any dominated strategies or an elimination of dominated strategies does not yield a unique outcome. In such cases, a different way to ﬁnd a solution to the game is to be used. For each strategy of one player, the best response of the other has to be considered. Each and every move of one player has to be evaluated to ﬁnd the best possible choice. Using this method, called the best-response analysis for every player, all possible Nash equilibria of a game can be located. (Dixit, Skeath, & Reiley, 2015, p. 106) Deﬁnition 4 [BEST RESPONSE]: Let s−i be a strategy vector of all the players not including player i. Player i’s strategy si is termed a best reply to s−i if ui(si, s−i) = max ti∈Si ui(ti, s−i). (Maschler et al., 2013, p. 97) 3.3 Nash Equilibrium In cases where players’ strategies are best responses to each other, in other words, if the players have "mutual best responses", where no one has an incentive to deviate from his strategy, the term Nash equilibrium2is used in this terminal point of the game. (Watson, 2013, p. 97) Figure 9 shows a game in strategic-form without any dominated strate- gies. The seller prefers coffee while the tourist prefers tea, but for both of them it is important that they drink the same beverage. If the tourist chooses "Coffee", the seller’s best response is "Coffee", but if he chooses "Tea", the best response will be "Tea" and vice versa. The two pairs of strategy (Coffee, Coffee) and (Tea, Tea) both satisfy a stability property. Neither player has a reason to deviate, because given the other player’s strategy, no deviation will grant a higher payoff. 2Nobel laureate John Nash is the "father" of the equilibrium concept which he reported in Non-Cooperative Games, Annals of Mathematics, 1951.
- 27. 3.3. NASH EQUILIBRIUM 13 Seller Tourist Coffee Tea Coffee (10,5) (2,2) Tea (0,0) (5,10) Figure 9: Tea or Coffee Deﬁnition 5 [NASH EQUILIBRIUM]: The strategy vector s∗ = (s∗ 1, ..., s∗ n) is a Nash equilibrium if s∗ i is a best reply to s∗ −i for every player i ∈ N. (Maschler et al., 2013, p. 96-97)
- 28. 14 CHAPTER 3. DOMINANCE, BEST RESPONSE & NE
- 29. Chapter 4 Equilibrium Reﬁnements T he Nash equilibrium is the most important solution concept in game theory, but often games have more than just one Nash equi- librium. In those games the intention is to ﬁnd out which equilibria are more reasonable than others. In this chapter, some equilibrium re- ﬁnements will be introduced presenting solution concepts which disclose differences between Nash equilibria. One of the solution concepts for extensive-form games is the subgame perfect equilibrium, which will be explained in Section 4.2. The idea behind this method is to ﬁnd non-credible threats.1 This equilibrium can be found using backward induction. 4.1 Backward Induction The following two sections are based on (Fudenberg & Tirole, 1991, p. 93-94) and (Watson, 2013, p. 186-89). Selten (1965) was the ﬁrst who argued that some equilibria are "more reasonable" than others. Figure 10 is a ﬁnite game of perfect information. The backward induction procedure requires analysing a game from the leaves to the root. At the last decision node in the game, the tourist needs to decide which of his strategy is best 1These threats are non-credible because their goal is to deter deviations by using "irrational" behaviour off the equilibrium path. 15
- 30. 16 CHAPTER 4. EQUILIBRIUM REFINEMENTS for him at this point downwards. He will choose "Go in" which reduces the game for the seller to the same size the tourist had. The seller now can decide between a payoff of 2 for "Wait" and a payoff of 3 for "Lure", since he can be sure to have an opponent2 who is rational and who will deﬁnitely choose strategy "Go in". Using this method, it is easy to ﬁnd one of two Nash equilibria highlighted yellow in Figure 10’s strategic-form and red in the extensive-form.3 The other Nash equilibrium is stable as well, because if the seller chooses "Wait" in the ﬁrst place, the tourist’s decision node will never be reached and therefore he loses nothing by playing strategy "Stay out". Nevertheless, in Selten’s opinion, this equilibrium is suspect. If the tourist’s information set is reached, he should play "Go in" and therefore he always should choose this strategy. As a consequence, the seller could anticipate this behaviour and choose "Lure". This would lead to a higher payoff for both players. This is the reason the equilibrium (Wait, Stay out) is not "credible", because its foundation is an empty threat by the tourist to play "Stay out", which he would never wish to carry out. In conclusion, there is always a pure-strategy Nash equilibrium in a ﬁnite game with perfect information, which can be found through backward induction. 4.2 Subgame Perfect Equilibrium In the last information set of the game illustrated in Figure 11, none of the strategies are dominated for the tourist. Here it is not possible to use backward induction. If only the game starting at node z is considered, the game would be a zero-sum simultanious-move game with one unique Nash equilibrium having expected payoffs of (0,0). Now the whole game starting at node z can be consolidated and replaced by its expected payoff. This reduces the tree to the one in Figure 10. Players do not always select their best responses ex ante. They make a rational decision when it is their 2The word opponent is often used to describe other players, but there are games requiring cooperative behaviour where this terminology is not appropriate. 3The red path is also called the equilibrium path.
- 31. 4.2. SUBGAME PERFECT EQUILIBRIUM 17 Seller (2, 0) Wait Tourist (3, 1) Go in (0, 0) Stay out Lure Seller Tourist Go in Stay out Wait (2,0) (2,0) Lure (3,1) (0,0) Figure 10: Non-credible Nash equilibrium move to take action. This is called sequential rationality. Deﬁnition 6 [SEQUENTIAL RATIONALITY]: An optimal strategy for a player should maximize his or her expected payoff, condidtional on every infor- mation set at which this player has the move. That is, player i’s strategy should specify an optimal action from each of player i’s information sets, even those that player i does not believe (ex ante) will be reached in the game. The logic behind subgame perfection is exactly that: Replace any proper subgame4 by one of its Nash equilibrium payoffs and replace it in the tree. After that, execute backward induction on the reduced tree. Deﬁnition 7 [SUBGAME]: Given an extensive-form game, a node x in the tree is said to initiate a subgame if neither x nor any of its successors are in an information set that contains nodes that are not successors of x. A subgame is the tree structure deﬁned by such node x and its successors. Considering Deﬁnition 7 the game trees below the nodes x, y and z can be identiﬁed as subgames, but not below α. 4Subgames that do not start from the root are called proper subgames.
- 32. 18 CHAPTER 4. EQUILIBRIUM REFINEMENTS Seller x (2, 0) Wait Tourist y (3, 1) Go in Seller z α (2, −2) C (−2, 2) D A α (−2, 2) C (2, −2) D B Stay out Lure Tourist Figure 11: Subgame perfect Nash equilibrium Deﬁnition 8 [SUBGAME PERFECT NASH EQUILIBRIUM]: A strategy proﬁle is called a subgame perfect Nash equilibrium (SPE) if it speciﬁes a Nash equilibrium in every subgame of the original game. According to Deﬁnition 8, it can be stated that if the whole game is its only subgame, the sets of Nash equilibria and SPE will coincide, but if there is more than one subgame, some Nash equilibria may fail to meet the criteria of a SPE.
- 33. Chapter 5 Games with Incomplete Information T his chapter will focus on games with incomplete information introduc- ing the concepts of beliefs and knowledge. A game with incomplete information is a game where players do not have complete infor- mation about the game. They may not know other players’ payoffs. For instance, a seller does not know how much a potential customer values an item and the customer probably does not know how much an item costs to produce or how much rent the vendor pays for his shop. The same situation does apply for games where dice are involved. In order to model such games, information about the players’ beliefs and their knowledge with the whole hierarchy of knowledge is needed.1 John Harsanyi’s inno- vation (1967) of introducing a ﬁctional new player to the game resulted in the possibility to transform games with incomplete information to a game with imperfect information. (Williams, (2013), p. 169; Maschler et al., (2013), p. 319) 1It is necessay to have information about every player’s knowledge of the knowledge of other players, knowledge of the knowledge of the other player’s knowledge of other players, and so on. 19
- 34. 20 CHAPTER 5. GAMES WITH INCOMPLETE INFORMATION 5.1 Belief, Knowledge and Sequential Equilibrium This section concentrates on another equilibrium concept for extensive- form games. Other than the subgame perfect equilibrium concept, where it can be determined if a player’s action is rational for every subgame, this concepts focus on games where such an approach is not possible. In many games, players do not exactly know in which particular vertex they are located. It is likely that the whole game is one big subgame and there are no other subgames than the game itself. In such games, the players need to form beliefs on how probable it is to be located at one node in an information set and how strategies based on these beliefs will affect the rest of the game. In this kind of games where a player is confronted with multiple nodes in one information set, a player’s beliefs are speciﬁed as a probability distribution p (0 ≤ p ≤ 1) over nodes in the information set, which deﬁne how probable it is to have reached that speciﬁc node. Based on the probability distribution p, a player must choose a sequentially rational strategy. This means that given some beliefs, a player must choose the strategy which gives him the highest expected payoff. (Williams, 2013, p.170-171) (Maschler et al., 2013, p. 271) Consider Figure 12 in which the seller does not know what kind of tourist he is dealing with. The seller assumes that every tourist who enters his shop has a 70 percent probability of being eager to buy. To act sequentially rational, a player must maximise his expected payoff at each information set. (Williams, 2013, p.171) For instance, the tourist in Figure 12 should always choose "Buy" in his information set on the left hand side, because "Not" is dominated by "Buy". The seller knows this and would thereby choose action "High" at his left vertex, which he reaches with probability p = 0.7. On the right hand side, it may seem like the tourist should choose strategy "Buy’" when the game reaches his decision set, but given his beliefs it is better for him to do the opposite. In fact, by looking closer it can be observed that strategy
- 35. 5.1. BELIEF, KNOWLEDGE AND SEQUENTIAL EQUILIBRIUM 21 Nature (10, 10) Buy (0, 0) Not High (5, 20) Buy (0, 0) Not Low p = 0.7 eager to buy (10, −5) Buy’ (0, 0) Not’ High (5, 10) Buy’ (0, 0) Not’ Low p = 0.3 Not Seller Tourist Tourist Figure 12: Sequential rationality "High" weakly dominates strategy "Low". Looking at Figure 12’s strategic- form in Figure 13, where the expected payoffs are already calculated, his best strategy is visibly revealed. Considering the strategy proﬁle (High, BuyBuy’), with probability 0.7 there is (High, Buy) on the left hand side and with probability 0.3 (High, Buy’) on the right hand side. This equals in an ex ante expected payoff of 0.7 × 10 + 0.3 × 10 = 10 for the seller and 0.7 × 10 + 0.3 × (−5) = 5.5 for the tourist. Seller Tourist Buy Not High (10,10) (0,0) Low (5,20) (0,0) Seller Tourist Buy’ Not’ High (10,-5) (0,0) Low (5,10) (0,0) Seller Tourist BuyBuy’ BuyNot’ NotBuy’ NotNot’ High (10,5.5) (7,7) (3,1.5) (0,0) Low (5,17) (3.5,14) (1.5,3) (0,0) Figure 13: Strategic-form of Figure 12
- 36. 22 CHAPTER 5. GAMES WITH INCOMPLETE INFORMATION 5.2 Bayesian Nash Equilibrium To form a Bayesian Nash equilibirum, which is the Nash equilibrium of a game with incomplete information, a strategy proﬁle and a set of beliefs for every player is always necessary. The players are not only required to choose credible strategies, but to hold reasonable beliefs. The Bayesian equilibrium, which is a generalisation of a sequential equilibrium differs only in the way how beliefs are modelled. A Bayesian equilibrium must assume a weak consistency of beliefs. This means that for every information set in the game which is reached with a positive probability, beliefs are deﬁned by Bayes’ rule. Information sets which are reached with positive probability are on the equilibrium path, if its probability is 0, it is off the equilibrium path. (Kreps and Wilson, (1982); Fudenberg and Tirole, (1991), p. 209-215) Deﬁnition 9 "A Static Bayesian Game consists of: • The set of players I. • For each player i: – a set of possible types Ti – set of actions Ai • Payoffs which depend on the actions taken by all players and types: ∀i ∈ I, ui : A × T → R • Probability measure on types p : T → [0, 1] • All these elements are common knowledge." (Sáez Martí, 2015b) Figure 14 will be used to explain Bayes’ rule. Imagine a tourist shows interest in a product 60 percent of the time and a seller is able to observe that. Thus, the seller will mention a higher price for that product 90 percent of the time. The seller’s behaviour is fundamentally subordinate to the tourist’s interest. The probabilities on the different leaves are based on prior beliefs. For instance, if the seller realises that the tourist is
- 37. 5.2. BAYESIAN NASH EQUILIBRIUM 23 interested, he will offer a high price, producing a conditional probability of Pr(I0 | H1). This conditional probability is also called posterior probability and is equal to: Pr(I0 | H1) = I0∩H1 Pr(H1) , Pr(H1) > 0, (1) where I0 ∩ H1 is the probability that A and B both happen. The equation above can be transformed into Pr(I0 | H1) = Pr(I0 | H1)Pr(H1) = Pr(H1 | I0)Pr(I0) Pr(I0 | H1) = Pr(H1 | I0)Pr(I0) Pr(H1) = Pr(H1 | I0)Pr(I0) Pr(H1 | I0)Pr(I0) + Pr(H1 | U0)Pr(U0) , (2) which is called the Bayes’ rule. (Williams, 2013, p. 188-189) Deﬁnition 10 [BAYESIAN NASH EQUILIBRIUM]: In a static Bayesian Game the stratgies s∗ = (s∗ 1, ..., s∗ n) form a (pure-) strategy Bayesian Nash equilibrium if for each player i and for each of i s types ti ∈ Ti, no player wants to change his strategy, even if the change involves only one action by one type. (Sáez Martí, 2015b)
- 38. 24 CHAPTER 5. GAMES WITH INCOMPLETE INFORMATION Nature Seller High 0.9 Low 0.1 Interested tourist=0.6 Seller High 0.5 Low 0.5 Uninterested tourist=0.4 Nature I0 U0 Seller Pr(H1 | I0) = 0.54 H1 0.9 Pr(L1 | I0) = 0.06 L1 0.1 Pr(I0) = 0.6 Seller Pr(H1 | U0) = 0.2 H1 0.5 Pr(L1 | U0) = 0.2 L1 0.5 Pr(U0) = 0.4 Figure 14: Conditional probabilities
- 39. Chapter 6 Cooperative Bargaining A ll previous chapters were presented to introduce the reader to basic principles of game theory and to give the necessary knowledge to understand the following chapters which build the core of the research conducted. There is an immense amount of literature based on the topic of bargaining published in the last decade. Most of it concentrates on extensive-form games that represent important aspects of trading. Thus, there is a growing number of individuals who think critical about game theoretic predictions, because these cannot be used in general for economic theory. Nevertheless, the importance of studying bargaining in real-world settings has become well recognised and is taught by major business schools. In this chapter, bilateral bargaining theory will be presented, which models situations in which two players negotiate toward an agreed-upon outcome. All bargaining games have two characteristics in common. On one hand, the total payoff they could reach by achieving an agreement is bigger than the payoff they could gain separately. On the other hand, the negotiation is about how the existing surplus should be divided. Each bargainer tries to get the most out of the negotiation for himself, while facing the threat of ending up with no surplus if an agreement fails. This threat causes bargaining to be a very strategic matter. First, basic deﬁnitions and concepts of bargaining games will be determined to then focus on the cooperative Nash bargaining solution and 25
- 40. 26 CHAPTER 6. COOPERATIVE BARGAINING its properties. This solution concept is a function that assigns an outcome to every game that one could think of as a recommended outcome by an arbitrator or judge. (Dixit et al., (2015), p. 663-64; Chatterjee, (2014), p. 190) 6.1 The model The following model of bilateral bargaining games1 with N = (1, 2) was ﬁrst presented and studied by Nash (1950) using a set S ⊆ R2 and a vector d = (d1, d2) ∈ R2. The players try to reach an unanimous agreement on some possible bargaining outcome x = (x1, x2) ∈ S. The outcome is expressed as units of utility and in our examples as units of money, where xi is player i’s utility from the outcome. The set S represents all possible bargaining outcomes and the disagreement outcome or disagreement point2 d results if no agreement is achieved from the bargaining process. Each player i has a preference ordering i over the set of lotteries over S ∪ {D}. Note that it is assumed that bargainers satisfy the von Neumann and Morgenstern assumptions.3 (Maschler et al., (2013), p. 622; Sáez Martí, (2015a)) Deﬁnition 11 A [BARGAINING GAME] for N is a pair (S,d) where • S is a nonempty, compact, and convex subset of RN, • d ∈ S, • There exitsts an alternative x = (x1, x2) ∈ S satisfying x d. • The set of all bargaining problems is denoted by B. • The function f : B → R2 assigns to each bargainin problem (S,d) a unique element in S. 1It will be exclusively focused on games with two players but the reader should be aware of games with multiple players. 2It is also called BATNA (best alternative of a negotiated agreement by the Harvard Negotiation Project (Dixit et al., 2015, p. 666)) 3The four axioms are completeness, transitivity, continuity, and independence.
- 41. 6.2. NASH BARGAINING 27 (Peters, (1992), p. 2; Maschler et al., (2013), p. 625) 6.2 Nash Bargaining 6.2.1 Nash Axioms This section, which is based on (Napel, 2002, p.12), (Maschler et al., 2013, p. 627-30) and (Muthoo, 1999, p. 31-32), presents the four axioms which were ﬁrst proposed by Nash (1953). These axioms are mathematical expressions, which should be used to ﬁnd a bargaining agreement. The unique solution concept presented in the next section satisﬁes these properties. Invariance to Equivalent Utility Representations (INV) Two bargaining problems (S, d), (S , d ) ∈ B should deliver the same solution, if their utilities are changed according to positive afﬁne trans- formations. For instance, whenever τ(u) = αxi + β for constants α, β ∈ R and α > 0, then Axiom 1 f (τ(S), τ(d)) = τ(f (S, d)). This is equivalent to a change of units from dollars to cents. It is reasonable to require that a different representation should not change the solution. Thus, although the bargaining solution of these two problems differ, they must be related in the speciﬁed way. Pareto Efﬁciency (PAR) The second Axiom implies that a bargaining agreement is reached. The goal is to get the best possible outcome for the players. Therefore, an alternative solution cannot exist, where one player gets a higher output without decreasing the other player’s outcome.4 4This stands for Pareto efﬁciency, named after the Italian economist Vilfredo Pareto (1848-1923). In his book Manuale di Economia Politica he developed the idea that the distribution of resources is not optimal if it is possible to increase at least one person’s welfare without harming the interests of any other individual.
- 42. 28 CHAPTER 6. COOPERATIVE BARGAINING Axiom 2 We ﬁx (S, d) ∈ B and a bargaining solution f : B → R2. To have Pareto efﬁciency there does not exist any utility pair (x1, x2) ∈ S ∪ {d}, such that xi > fi(S, d). Symmetrie (SYM) A bargaining game (S, d) ∈ B is symmetric if d1 = d2, and (x1, x2) ∈ S if and only if (x2, x1) ∈ S. If this is the case, then both players should be treated equally. Axiom 3 f1(S, d) = f2(S, d) Indipendence of Irrelevant Alternatives (IIA) The last axiom declares that options which are not selected should not change the solution when they are removed. For every bargaining game f (S, d) ∈ S and every subset S ⊆ T, Axiom 4 f (T, d) ∈ S → f (S.d) = f (T, d). 6.2.2 The Nash Bargaining Solution The four axioms showed above lead to the Nash bargaining solution. Theorem 1 There is a unique bargaining solution concept N for the family B → R2 satisfying INV, PAR, SYM and IIA. It is given by f N(S, d) = arg max x∈S,x≥d (x1 − d1)(x2 − d2). (3) Considering Figure 15, the solution N (S, d) maximises the area of the rectangle with bottom left vertex d and top right vertex x. N (S, d) is the Nash bargaining solution5 of the bargaining game (S, d). For every point x ∈ S with x ≥ d, the area of the rectangle is the product of f (x) = (x1 − d1)(x2 − d2) which is called the Nash product. (Maschler et al., 2013, p.630-31) 5It is also called the Nash agreement point.
- 43. 6.2. NASH BARGAINING 29 N (S, d)S d Figure 15: The Nash bargaining solution Imagine a family in their holidays in Turkey. This family has two children, Sebastian and Doreen. Their father offers them 100 dollars for shopping, if they can achieve an agreement on how to split this amount between each other. If no agreement is reached, Sebastian and his sister will both get 25 dollars each. 25 + 25 < 100, so there is clearly a surplus from agreement. If this was not the case, both, Sebastian and Doreen, would take their outside opportunities and no bargaining would take place. When there is a surplus, consider the rule: each of the two children is given his disagreement outcome plus a share of the surplus. This share is depending on their relative bargaining strengths, which will be discussed later in this chapter. Considering Axiom 3, the share must be 1 2 each to achieve symmetry. Using equation 3 of the Nash bargaining solution, the result is: arg max x1 (x1 − d1)((100 − x1) − d2) = arg max x1 (x1 − 25)((100 − x1) − 25) FOC : x1 = 50 → x2 = 50 f N (S, d) = (50, 50) (4) A geometric representation of the Nash solution is shown in Figure 16. The disagreement point is in d, all points (x1, x2) on the blue line divide the gains in proportions 1/2 1/2 = 1 1 between Sebastian and Doreen and all points on the line from (0,100) to (100,0) use up the whole surplus. The
- 44. 30 CHAPTER 6. COOPERATIVE BARGAINING slope = 1/2 1/2 = 1 x1 + x2 = 100 fN (S,d) d Figure 16: The Nash bargaining solution in a simple way intersection between the blue and the black line is the Nash bargaining solution (50,50). Modifying this example in a way in which the father does not give both children the same amounts in case of disagreement, this would move the blue line up or down without changing its slope. Note that if one of the children is more risk averse6 the bargaining problem changes and the less risk averse child gets a higher share. It is important to be familiar with the cooperative Nash bargaining solution, but the most important model to examine behaviour at the Grand Bazaar is the non-cooperative model explained in the next chapter. (Dixit et al., 2015, p. 666-68) 6This would make his utility function more concave.
- 45. Chapter 7 Noncooperative Bargaining T his chapter will analyse the non-cooperative bargaining repre- sented by extensive-form games, being the basis for explanation of observed strategic behaviour at the Grand Bazaar. First, ultimatum games will be introduced by using a basic example and then attention will be aimed towards the non-cooperative Rubinstein’s basic alternating-offers model. This model will build a basic framework which can be extended and modiﬁed later on. 7.1 Ultimatum Games The simplest of bargaining models is the ultimatum bargaining game. It is a game where one player makes an offer and the other can accept or reject. This is the whole game in which all bargaining power is on the proposer’s side. Imagine a tourist at the Grand Bazaar likes one of the paintings in one of the stores. This painting was already in the store when the seller bought it from his predecessor and therefore has no value to him. Since the painting is worth $100 for the tourist and nothing for the seller, a trade would generate a surplus of $100. The price determines how this surplus is divided between these two players. There is a unique subgame perfect equilibrium in this game in which the tourist gets the painting for free. This standard ultimatum game is pictured in Figure 17. Note that 31
- 46. 32 CHAPTER 7. NONCOOPERATIVE BARGAINING Tourist 0 0 (1 − m, m) Accept (0, 0) Reject Seller 100 Figure 17: Ultimatum game the tourist can make any offer between 0 and 100, and that the seller then decides between the outcomes (100 − m, m) and (0, 0), where m stands for the tourist’s offer. (Watson, 2013, p. 244-45) By observing the game, one can recognise that this game has 100 × 100 = 10 000 subgames. One subgame for every different amount the tourist could offer to the seller. It seems obvious that the seller should accept every offer m > 0. Only when m = 0, rejection could be a best response for the seller. In a game like this, in which a smallest monetary unit exists (1 cent), the subgame perfect equilibrium is where the tourist offers the smallest possible amount and the seller accepts it (99.99, 0.01).1 The subgame perfect equilibrium is efﬁcient, because the whole surplus is shared between the players. (Watson, 2013, p. 245-46) 1Note that the unique subgame perfect equilibrium in a game without a smallest monetary amount would be (100,0), respectively 0 for the responder and the whole surplus for the proposer.
- 47. 7.2. RUBINSTEIN’S BASIC ALTERNATING-OFFERS MODEL 33 7.2 Rubinstein’s Basic Alternating-Offers Model The ultimatum game is a too simplistic model for most real-world nego- tiations. In reality, there are processes where players take turns to make offers to each other until an agreement is reached. Rubinstein’s model provides with several insights about bargaining situations. One insight is that bargaining processes without any costs for haggling are indeter- minate. Hence, not only players’ preferences, but also their combination with agreement times are crucial elements for sequential bargaining. Cross (1965, p.72) stated: If it did not matter when people agreed, it would not matter whether or not they agreed at all. This is intuitive since most people are impatient to some degree and do not prefer to bargain for too long. Additionally, most people discount future payoffs relative to the present. In game theoretic models, the motion of a discount factor δi ∈ (0, 1) is used. How someone discounts the future and how impatient someone is, will affect the surplus each negotiator gets. (Muthoo, (1999), p. 42; Watson, (2013), p. 246-47) The bargaining procedure will now be speciﬁed before modifying the previous ultimatum game to an alternating-offers game. Offers are made in particular points of time. Player A offers at time t∆2 when t is even (i.e., t = 2, 4, 6, ...) and Player B can accept or reject it. If he rejects, he can make a counteroffer in (t + 1) and Player A can decide whether he wants to accept or reject. If Player i accepts an offer for a share mi (0 ≤ mi ≤ π) of the surplus, Player i’s payoff will be mi × δt. (Muthoo, (1999), p. 42-43; Napel, (2002), p. 31) Now consider the ultimatum game in Figure 17 to have two periods with an additional discount factor for both players. Again, the tourist makes the ﬁrst offer and the seller can decide whether to accept or reject. If he rejects he can make a counteroffer. In the second period one ﬁnds 2∆ stands for any possible time frame (e.g. hour, day, week). It shall be noted that for simplicity and for the ease of reading, ∆ will not be used in following examples and will be replaced by 1 instead.
- 48. 34 CHAPTER 7. NONCOOPERATIVE BARGAINING himself back in an ultimatum game, but with reversed roles. The seller has the bargaining power now. If an agreement is reached in the second period, the payoffs are discounted relative to the ﬁrst period. Therefore the tourist would get m2δ1 and the seller (1 − m2)δ1. The extensive-form is on the left and the bargaining including the disagreement point are pictured on the right hand side. The outer line in the picture on the right represents the payoff vectors they could reach if they come to an agreement in the ﬁrst period. The inner line represents the same for the second period. It contains the discounted payoff vectors from the ﬁrst period. The subgame perfect equilibrium is easy to ﬁnd in this example. The solution for the ultimatum game in the second period was already shown in the previous section. Discounting these payoffs results in 0.01δ1 and 99.99δ2 as continuation values. Therefore, the seller should reject any offer m1 < 99.99δ2 and will be indifferent for m1 = 99.99δ2 but he will deﬁnitely accept if the tourist offers an amount m1 ≥ δ2. This leads to the unique Nash equilibrium of (1 − δ2, δ2). The right hand side of Figure 18 offers a graphical illustration of this equilibrium. (Watson, 2013, p. 247-50) Expanding this bargaining model of alternating-offers to a ﬁnite num- ber of periods T will not change anything in the solution ﬁnding process. It can be analysed in the exact same way. For every even number of periods, Player 2 will have the ﬁnal offer and for every odd number, Player 1 will have the last offer. In case of agreement in period t, the payoffs need to be discounted by δt−1 i . Note that patience is positively related to bargaining power. The closer a discount factor in Figure 18 gets to 0, the smaller a player’s payoff gets. One of the most interesting parts of this model is that modifying T does not change the fact that agreement is always reached in the ﬁrst period, where the biggest joint value is. (Watson, 2013, p. 249-50) This game can also be expanded to inﬁnite periods of T with the difference that backward induction is no longer possible. At this point, it is known that a subgame perfect equilibrium must satisfy the following two properties: Property 1 No Delay: Whenever a player has to make an offer, her equilibrium offer is accepted by the other player.
- 49. 7.2. RUBINSTEIN’S BASIC ALTERNATING-OFFERS MODEL 35 Tourist 0 0 (1 − m1, m1) Accept Seller 0 0 (m2, 1 − m2) Accept (0, 0) Reject Tourist 100 Reject Seller 100 u2 u1 d 100 δ1 100 δ2 1− δ2 Figure 18: A two-period game
- 50. 36 CHAPTER 7. NONCOOPERATIVE BARGAINING Property 2 Stationarity: In equilibrium, a player makes the same offer when- ever she has to make an offer. (Muthoo, 1999, p.44) Given Property 2, Player 1’s equilibrium offer should put Player 2 in a position where he is indifferent between accepting and rejecting. Like shown before, indifference means that δ2(1 − m1) = m2. This equation holds for both players and therefore δ1(1 − m2) = m1. Solving these equations results in m1 = δ1(1−δ2) 1−δ1δ2 and m2 = δ2(1−δ1) 1−δ2δ1 . (5) Given Property 1, an agreement must be reached in the ﬁrst period which leads to the unique subgame perfect equilibrium (x∗, y∗): x∗(δ1, δ2) = 1−δ2 1−δ1δ2 and y∗(δ1, δ2) = δ1(1−δ2) 1−δ1δ2 (6) (Muthoo, (1999), p. 43-45; Napel, (2002), p. 38-39) 7.3 Asymmetric Information In real bargaining situations at the Grand Bazaar at least one of the ne- gotiators has some relevant information which the other does not have. There are in general a variety of things that may be relevant to the bargain- ing outcome. The payoffs depend on players’ private information about their preferences and their reservation values.3 In this section, the role of asymmetric information on the bargaining outcome is studied, at which at least on of the player’s reservation values is his private information. The focus lies on a bargaining situation in which a seller owns an object that a tourist wants to buy. If an agreement is reached at a price p (p ≥ 0), the seller’s payoff will be p − c and the tourist’s payoff v − p, where c denotes 3The maximum price at which a buyer is willing to buy and the minimum price at which a seller is willing to sell.
- 51. 7.3. ASYMMETRIC INFORMATION 37 the seller’s reservation value4 and v denotes the tourist’s reservation value. In case of disagreement both players’ payoff is equal to zero.5 (Muthoo, 1999, p. 251-53) 7.3.1 One-Sided Uncertainty In this section, it is assumed that only one side has private information about their reservation value and that reservation values of the players are independent. This scenario is closer to reality, where an informed buyer could have information about production costs of offered goods and also about costs for rent which could reveal a seller’s reservation value. Inversely, a seller with all his experience also might have the ability to get information on a buyer’s reservation value, before negotiations even started. Furthermore, there is a possibility for both players to acquire in- formation about their opponents’ reservation value during the bargaining process. In contrast to the case where the player making offers has all the bargaining power, Muthoo (1999) has proven that if the opponent has private information, the payoffs of the offer-making player are adversely affected. He also studied the existence of a screening equilibrium in which the uninformed player gets information during the bargaining process about his opponent’s reservation value. Screening Equilibrium In this section, the results of Muthoo (1999) are analysed presenting the perfect Bayesian equilibrium (PBE) he found as a result. In order to do so, an introduction to some variables is needed. Consider a situation where player’s reservation values are independent and the seller’s reservation value is his private information. Let G be the seller’s reservation value which is uniformly distributed on the closed interval [0, 1]. The buyer be- lieves that the seller’s reservation value is less than or equal to c. Therefore, 4The sum of his cost of production and other expenses like rent, electricity and water. 5The seller still has to pay for expenses like rent, but for simplicity this factor is disregarded in one single bargaining process in a mass of many in one day.
- 52. 38 CHAPTER 7. NONCOOPERATIVE BARGAINING G symbolises the buyer’s prior beliefs. G’s maximum and minimum value are denoted by c and c, where c ≥ c ≥ 0. This leads to, G(c) = 1, G(c) = 0 if c ≤ c and G(c) ≥ 0 if c ≥ c. λ stands for the lowest value the buyer thinks the seller could have. For this example let the buyer’s reservation value be v = c. Muthoo came to the conclusion that there is a perfect Bayesian equilibrium which is deﬁned by the following two equations. pn = 1 − (1 − β)βn and λn = a − βn (n = 0, 1, 2, ...) (7) with α = 1 − √ 1 − δ β = 1− √ 1−δ δ 1 ≥ β ≥ α ≥ 0 (8) Note that along the equilibrium path, the prices are strictly increasing and agreement will be reached with probability 1. The higher a seller’s cost of production the more periods it takes until agreement is reached. The seller’s private information is in fact (partly) revealed during the bargain- ing process. This process resembles to an intertemporal price discrimination. Nevertheless, the equilibrium is inefﬁcient since trade does occur with positive probability after period 0. The bigger the discount factor gets, the higher the probability of offering a high enough price for the seller to accept the ﬁrst offer is. Furthermore, the buyer’s payoff gets closer to zero. However, for the research at the Grand Bazaar a small discount factor is more realistic, thus screening for privately held information is possible. Muthoo also proved that there is a continuum of PBE if v = c like in the example above, but there is a unique PBE if v > c and gains from trade exist with probability 1. (Muthoo, 1999, p. 272-82) The No Gap Case For the research at the Grand Bazaar one particular modiﬁcation may be important. When the time interval between two consecutive offers is arbitrarily small, the following theorem provides with a characterisation of the set of buyer payoffs sustainable as a PBE.
- 53. 7.3. ASYMMETRIC INFORMATION 39 Theorem 2 Assume that v = c, and that G is continuously distributed on the closed interval [c, c]. Let ˆuB be such that ˆuB ≥ (v − p)G(p) for all p ≥ 0. For any > 0 there exists a ∆ > 0 such that for any ∆ ≤ ∆ and any uB ∈ [ , ˆuB − ] there exists a PBE such that the buyer’s payoff equals to uB. This means that there exists a PBE in which an uninformed buyer could still get arbitrarily close to a payoff of ˆuB if the time interval is arbitrarily close. (Muthoo, 1999, p. 284-85) 7.3.2 Two-Sided Uncertainty Chatterjee and Samuelson (1987) proved that there is a unique Nash equilibrium in a situation with two-sided uncertainty. The model is characterised by the following: Valuation Discount factor Type Seller Buyer Seller Buyer Hard s b Ds Db Soft s b Ds Db where s ≤ b < s ≤ b and discount factors were drawn from the interval (0,1). They let π1 s be the initial probability that a seller o f unknown type is so f t and π1 b be the initial probability that a buyer o f unknown type is so f t They ﬁrst studied a model with two types of buyers and sellers in which they could be strong or weak and then expanded to a model in which the buyers and sellers could be any kind out of a continuum of types. Nevertheless, the extended model behaved similar to the ﬁrst one which led to following results: Theorem 3 Any of the potential gains s − b which are realized in the bargaining process accrue either entirely to the seller or entirely to the buyer. The buyer is more likely to receive these gains from trade if i π1 s is relatively large; π1 b small;
- 54. 40 CHAPTER 7. NONCOOPERATIVE BARGAINING πs small and πb large (equivalently [...] Ds small; Db large; b − s small and b − s large (given s − b)). The seller is more likely to receive the gains from trade under opposite conditions. (Chatterjee & Samuelson, 1987, p. 187) 7.4 Other Modiﬁcations The following three sections are based on (Muthoo, 1999, p. 73-74, 99-100, 137-38) 7.4.1 Risk of Breakdown There is a possibility that negotiations break down in a random manner. However, the risk of an "intervention" by a third party is negligibly small at the Grand Bazaar. The possibility that another seller could cause negotiations to break down is almost zero, because norms and manners do not allow such a behaviour. The risk of having a potential buyer in company of his wife or children who could cause negotiations to break down, for reasons like a sudden discovery of something interesting in an other store, is also negligible considering that bargaining process are generally short at the Bazaar. This leads to the cognition that the risk of breakdown can be disregarded in this thesis. (Küçükerman & Mortan, 2007, p. 70-71) 7.4.2 Outside Options Imagine a tourist shopping at the Grand Bazaar. He suddenly ﬁnds a nice piece of clothing at the ﬁrst store he walks in. After negotiation, he and the seller reach an agreement on the price. The tourist then decides to look around in the Bazaar ﬁrst and in case he cannot ﬁnd something similar which gives him the same value for a cheaper price, come back to the ﬁrst store and buy the piece for the agreed price. There are models which study the impact of such an outside option on further negotiations in
- 55. 7.5. REPUTATION EFFECTS 41 other stores. Nevertheless, for this study of the Grand Bazaar, this kind of modiﬁcations of the alternating-offers model can be ignored. The tourist in this example can never be sure to ﬁnd this piece he liked when he returns to the ﬁrst store. The seller could have sold it by then. There is also a possibility of the seller recognising the returning tourist and realising that he could not ﬁnd a better offer which in the worst case could result in increasing prices. It is also highly unlikely that a seller has an outside option like this, since he would sell his goods for an acceptable price and would not have the opportunity of waiting for a better paying customer while letting the ﬁrst one wait. 7.4.3 Inside Options Models with inside options contain bargaining over an indivisible good which has a utility to his owner in each period. For instance, if a seller and a buyer bargain over the price of a house, the seller still gets a utility of living in this house in each period as long as the bargaining goes on. Inside options are also not applicable for the Grand Bazaar, because sellers cannot gain a utility from their goods like in the example before. Even if some of them could, like the jewellers who could wear their accessories themselves, cleaning them afterwards would erase the gained utility right away. On the contrary, if there is an inside option for sellers it would be negatively correlated to their payoff, because they still have to pay the rent for their stores in case of disagreement. The buyers may have an inside option in the interest they get from their banks for keeping their money in their accounts, but the amount of interest they will get during the short period of negotiation at the Grand Bazaar is also negligible. 7.5 Reputation Effects There are many tourists at the Grand Bazaar of Istanbul, but there are quite a lot of local customers too. The difference to the foreign customers is that some of the locals are sent to a store by recommendation or they know
- 56. 42 CHAPTER 7. NONCOOPERATIVE BARGAINING the seller from previous transactions. In cases like these, the bargaining situation changes. The seller and the buyer ﬁnd themselves in a repeated bargaining game. The seller could try to build a reputation of having a good price-quality ratio. This could lead to potential new customers by recommendation and returning previous customers. Thereby, the seller should intuitively agree on lower prices to bind his customer and get a beneﬁt from future transactions.6 How much lower the price will be relative to the single-shot bargaining game, is dependent on the time intervals between transactions and the buyer’s ability to assure the seller of future transactions. (Fudenberg and Tirole, (1991), p. 416-21; Muthoo, (1999), p. 295-315) 6The idea behind it is that it is better to get 10 times a payoff of 1 than a payoff of 5 once.
- 57. Chapter 8 The Grand Bazaar of Istanbul T he Grand Bazaar1 of Istanbul is one of the largest and oldest bazaars in the world. It is located in the heart of Istanbul and can easily be reached by public transportation. It has 8 main entrances, 65 streets on an area of 40 000m2 and 3300 stores with 40’000 employees. It attracts up to 300’000 visitors a day and is therefore one of the most-visited tourist attractions worldwide.2 Although there are items sold coming out of serial production, the Bazaar still has some interesting, antique and unique goods to offer. This and its incomparable atmosphere still drives foreign and local visitors to the bazaar, looking for something to haggle about while drinking traditional Turkish tea. (Küçükerman & Mortan, 2007, p. 251) 1Its Turkish name is Kapalıçar¸sı which means "Covered Market". 2This data was published by the Turkish Ministry of Culture and Tourism in 2007 and the same information can be found on their ofﬁcial website (http://www.kultur.gov.tr/EN,113801/grand-bazaar.html), however the Grand Bazaars ofﬁcial website (http://www.grandbazaaristanbul.org/The_Grand_Bazaar.html) claims that there are 5000 shops and up to 400’000 visitors daily. Thus, a representative of the Association of Merchants at the Grand Bazaar claimed that there are approximately 3520 stores. 43
- 58. 44 CHAPTER 8. THE GRAND BAZAAR OF ISTANBUL 8.1 History Mehmed the conqueror, who was an Ottoman sultan and ruled from 1444 to 1446 and from 1451 to 1481, gave the order to build the Cevahir Bedesten (Bedesten of gems) in winter 1455/56. The construction of this building which today forms the core of the Grand Bazaar, ended in winter 1461/62. Although the architecture is purely Ottoman, there is a relief of a Byzantine eagle on top of the East Gate, which always gave space for interpretation whether or not the building could have been Byzantine beforehand. Despite some ﬁres during its history, the stores in the Cevahir Bedesten are still built out of wood. Only the most valuable goods were traded in this Bedesten because it was possible to lock the Bedesten and the stores were only open at certain times a day. (Küçükerman & Mortan, 2007, p. 162) The ﬁrst ﬁre happened in 1515 and shortly after, a second covered market called the Sandal Bedesten was built from 1545 to 1550. This led to a movement of textiles to the Grand Bazaar. Soon a lot of businesses surrounded both markets and ﬁnally the gap between them was closed. The Grand Bazaar reached its ﬁnal shape in the beginning of the 17th century. The concentration of commerce to this area caused recurring ﬁres throughout the history of the Grand Bazaar.3 In 18th century, after the big ﬁre of 1730, Ibrahim Pasa4 decided to renew the burnt areas of the Grand Bazaar and to change the wood in the stores to masonry. He also decided to cover several markets between the Bedestens with vaults. (Küçükerman & Mortan, 2007, p. 162) The Grand Bazaar was an exceptional and incomparable market until the ﬁrst half of the 19th century. The beginning of industrial revolution in Great Britain and the newly discovered possibilities of mass production in the textile industry caused a decline for the prosperous market’s economy. (Küçükerman & Mortan, 2007, p. 172-215) 3In the years 1548, 1588, 1618, 1645, 4658, 1660, 1687, 1688, 1730, 1750, 1766, 1791, 1943 and 1954 are documented ﬁres. 4He was the ﬁrst Grand Vizier of the Ottoman Empire appointed by Sultan Suleiman the Magniﬁcent.
- 59. 8.1. HISTORY 45 In 1894, a strong earthquake shattered Istanbul. The Bazaar took big damage and as a consequence one of the most important markets, the second-hand Bazaar, became an open-sky road. In 1914, the city of Istanbul bought the Sandal Bedesten and turned it into an auction house for carpets, due to a situation of devastation of the merchants of textile goods. (Küçükerman & Mortan, 2007, p. 162, 222-24, 238-39) Figure 19: Life at the Grand Bazaar in the 19th century (Küçükerman & Mortan, 2007, p. 217)
- 60. 46 CHAPTER 8. THE GRAND BAZAAR OF ISTANBUL 8.2 Merchants at the Grand Bazaar The merchants at the Grand Bazaar were sitting along both sides on wooden divans in front of their stores. A potential customer could sit next to the seller and talk together while drinking tea or Turkish coffee with him. There are still some merchants sitting in front of their stores and holding up the tradition. However, back in time the atmosphere was more relaxed, whereas nowadays the rush of modern civilisation found its way into the Bazaar. Until the restoration following the earthquake of 1894, the merchants of one good were compulsorily concentrated on one street which got its name by the merchants’ professions. The Cevahir Bedesten hosted jewellers, armourers and crystal dealers, while the Sandal Bedesten was the center for textiles. This kind of separation did disappear partially, but there is still a remarkable concentration of the same businesses along certain roads. (Gülersoy, 1980, p. 18-34) The ethics of the merchants changed drastically over time. Until the ﬁrst half of the 19th century the merchants were indifferent to proﬁt, there was no envy between the sellers and only one single and fair price was offered to their customers. This behaviour was due to the ethics of Islam and a social security system provided by the guilds. The guilds were taking care of their members for a monthly fee. They lost importance during the 19th century and were abolished in 1913. Since 1952, there exists an Association of Merchants of the Grand Bazaar, although it does not represent all of the merchants. Alongside with westernisation, mercantile ethics found their way to Ottoman society and today’s merchants at the Grand Bazaar are driven by proﬁt in the same way Western traders are. (Gülersoy, 1980, p. 43-48) (The ofﬁcial Grand Bazaar website, 2016)
- 61. Chapter 9 The Field Research The goal of the research at the Grand Bazaar was to study bargaining behaviour of its merchants. The most obvious path would have been to observe as many as possible bargaining situations and concentrate on some speciﬁc details. However, an approach like this was not possible during the time this research was conducted. It was off-season in February and Istanbul was target of terrorist attacks the months before, which caused many tourists to stay away from Istanbul and its crowded places. The sellers claimed that this was the worst February since 30 years. Besides, sellers preferred their stores to be empty while potential customers were around. They tried to avoid any distraction which meant that observation was not possible. 9.1 Questionnaire and Conduction Therefore, another approach was followed which took advantage of the current situation. A questionnaire was created which intended to acquire knowledge about the inﬂuence of a buyers’ characteristics on the price setting of the sellers. The goal was to collect information about sellers’ behaviour regarding possible disclosure of buyers’ reservation values. 47
- 62. 48 CHAPTER 9. THE FIELD RESEARCH In the ﬁrst question of the questionnaire, the sellers were asked to scale the following attributes’ importance from 1 to 10. 1 = (absolutely unimportant) and 10 = (extremely important) indicated the importance in regards to the price setting. • Age • Nationality • Gender • Interest in product • Wearing apparel • Accent • Sympathy • Number of articles • Time • Date • Receipt • Cash Additionally, at the end of this section, some empty rows were added. The merchants had the possibility to add some uncovered characteristics which were not included in this list. It must be noted that "receipt" and "cash" are different from the other attributes. Those are characteristics which a buyer can add to his proﬁle during negotiations. It does not reveal information about his reservation value, thus it may have inﬂuence on the price. The second section of the questionnaire put focus on the relation of characteristics to a difference in price settings. Knowing that the time of the day is relevant to a seller’s price setting is not sufﬁcient. It is important to know if it affects it positively or negatively for the customer. The sellers were asked to mark each of the following statements with the number which describes best how they feel about it from 1 to 5, with: 1 = strongly disagree, 2 = disagree, 3 = neither agree nor disagree, 4 = agree and 5 = strongly agree.
- 63. 9.1. QUESTIONNAIRE AND CONDUCTION 49 • The older the customer is, the lower the price gets. • A foreign customer gets a higher price than a local. • A female customer gets a higher price than a male. • The more interest a customer shows in a product, the higher the price gets. • The better dressed a customer is, the higher the price gets. • The better a customer’s Turk- ish is, the lower the price gets. • The friendlier a customer is, the lower the price gets. • The more articles a customer wants to buy, the lower the price gets. • The later the time of the day is, the lower the price gets. • The price is lower off-season. • The price is lower if the cus- tomer pays in cash. The third section of the questionnaire examines the sellers’ price ranges. They were asked to declare how much proﬁt they make from one item at least, which was equivalent to their reservation value. Another goal was to gain insights into how much proﬁt they make at most. These two pieces of information deﬁned an interval of possible points of agreement a particular seller had reached with different customers. The third part of this question asked how much they were willing to decrease the initial price they had set during negotiations. The information gained from this question could indicate the importance of an initial price setting and therefore, how important it is for a potential customer not to reveal any information about their reservation values. In the forth section of the questionnaire, the sellers were asked to disclose some private information for statistical purposes: - their age. - their gender. - what kind of product they sell. - how many years of experience they have. - whether or not they own the store they are working in.
- 64. 50 CHAPTER 9. THE FIELD RESEARCH Conducting the survey alone resulted in moderate success. The mer- chants were not willing to take part in a survey like that with a person they did not know and from whom they could not expect to get something in return. Numan Hocaosmano˘glu, a member of the Istanbul Chamber of Commerce, involved two of his colleagues, Ilhami Yazıcı1 and Mustafa ¸Senocak2 into the research. Both of them had an immense amount of inﬂuence in the Grand Bazaar. With their help, assistance by either a known member of the Association of Merchants at the Grand Bazaar (Ilker Yılmaz) or a police ofﬁcer (Mehmet Yıldız) was provided to conduct the survey. This eased the contact to the merchants and consequently the surveying process immeasurably. Thanks to Ilker Yılmaz, actual information about the distribution of the different sellers in the Bazaar was gained. This enabled the possibility to concentrate on surveying at least 5 percent of all merchants of each different sector to achieve statistically signiﬁcant results. 57 jewellers3, 19 carpet dealers, 27 textile dealers, 26 leather dealers and 47 sellers of gifts were interviewed, resulting in a total number of 176 conducted surveys. 9.2 Results The programming language R and an integrated development environ- ment called R-Studio was used for the evaluation of the data. Snippets of the R-code can be found in the appendix. Having a data matrix with 177 observations and 31 parameters, the analysis of the data was started by clustering the sellers into different groups. First, they were clustered into the groups of the goods they were selling and then differentiated by shop owners and employees to encounter possible differences between the 1Member of the Board of Directors of the Association of Merchants at the Grand Bazaar and Founder and CEO of the Yazıcı Group, one of the biggest enterprises in the gold market with a revenue of 600 millions Turkish Lira. (www.ito.org.tr/wps/portal/gazete- detay?WCM_GLOBAL_CONTEXT=ito_portal_tr/ito-portal/gazete/gzt-2014/gzt-2014- 9/gzt-2014-9-26/edd1de004608108898a9bb6b36283c4f) 2President of Leather and Leather Products Exporters’ Union 3Combines gold, silver and copper sellers.
- 65. 9.2. RESULTS 51 Table 1: Size of clusters Groups Number Groups Number Jewellery sellers (J) 57 J ∩ O 18 Carpet sellers (C) 19 J ∩ E 39 Textile sellers (T) 27 C ∩ O 8 Leather sellers (L) 26 C ∩ E 11 Gift sellers (G) 47 T ∩ O 13 Shop owners (O) 75 T ∩ E 14 Employees (E) 101 L ∩ O 10 L ∩ E 16 G ∩ O 26 G ∩ E 21 groups. This clustering would possibly give some insights into how their motivation could inﬂuence price settings (short term gains-employee vs. long term gains-owner). Histograms were created to analyse the data of the ﬁrst section of the questionnaire looking for certain trends. The results of this ﬁrst step can be separated in three groups. Characteristics which seem to be important, those which seem to be unimportant and those who need a closer analysis due to a high density of answers on both extremes. There was no buyer’s attribute which seemed to be mediocre important for all respondents. The peaks are always on the outer extremes, which was an expected result. In the following sections different levels are referred to. The ﬁrst level is without clustering. In the second level the data is clustered into different goods OR owners and employees and in the third level the data is clustered into different goods AND owners and employees. All the histograms can be found in the appendix. At this point, it must be noted that there must be a reasonable amount of doubt regarding the merchants’ answers to these questions. It is pos- sible that some of them were not faithfully answering. They demanded justiﬁcation for the questions, explanation of motives and intentions with
- 66. 52 CHAPTER 9. THE FIELD RESEARCH Table 2: Mean and standard deviation of the characteristics Statistic N Mean Median St. Dev. Inﬂuence of age 176 4.222 4.50 3.195 Inﬂuence of nationality 176 5.534 6.00 3.547 Inﬂuence of gender 176 3.551 1.00 3.122 Inﬂuence of interest for a product 176 6.080 7.00 3.678 Inﬂuence of wearing apparel 176 5.233 5.00 3.572 Inﬂuence of accent 176 3.869 3.00 3.169 Inﬂuence of sympathy 176 6.676 8.00 3.378 Inﬂuence of number of articles 176 7.250 8.00 2.877 Inﬂuence of time of the day 176 4.000 2.00 3.406 Inﬂuence of date 176 3.688 2.00 3.234 Inﬂuence of wanting a receipt 176 2.943 1.00 3.006 Inﬂuence of paying cash 176 5.205 5.00 3.656 the results. The merchants were clearly scared of people who could harm them and their businesses. They were scared that the data could be sold to travel agencies who would use the collected data for their customers. The sellers stated that they are often confronted with tourists using modern technologies in form of their smart phones to ﬁnd out at which stores in the Bazaar they can get the best prices. Apparently some tourists seem to know exactly for what prices some previous goods were sold. This aggravates the sellers’ negotiation by a remarkable amount. Therefore, the following results should be kept in perspective. Age More than 63% of all merchants gave an answer of 5 or below at the ﬁrst section of the questionnaire and looking at its histogram, a clear peak at 1 is observable. Going one level deeper in which the results are clustered to the different type of goods, a big difference is not noticeable. The results do not change by clustering to owner and employee either. Only when clustered one step further and looking at the data on a third level in which the data for different goods are clustered again to owners and employees.
- 67. 9.2. RESULTS 53 It is observable that owners of leather stores and employees of textile stores think that age can have an effect to the price. It must be noted that this does not mean they think age has a big impact on the price, only that in some cases it can be important. Gift shop employees did not agree with each other either. Some of the merchants argued that they are aware of the fact, that some young customers do not have the same amount of money like adults do. Therefore, age can have an impact on the price settings. One textile seller even remarked that some of the sellers at the Bazaar give discounts to students. Nationality There was some dissent on this issue. The merchants were separated into two groups. Almost 50% of the sellers answered with 5 or less. This is clearly a characteristic which needs to be analysed on deeper levels. On the second level, nationality seems to affect the price most for the gift and leather sellers. It is also more important to employees than to shop owners. On the third level, the results show that a foreign customer should beware of textile and leather shop employees and also generally in gift shops. The probably most remarkable result is concerning the carpet store owners, whose majority thinks that nationality affects the price a lot, but a big majority answered at the second section of the questionnaire, that this does not mean automatically that the price rises when a customer is foreign. Conversations with the sellers concluded that they do differentiate between nationalities. Turkish customers are often paying more for a carpet than foreigners. During the interviews with the different sellers, it was remarkable how some of them were a little offended and felt accused of being a hustler while others admitted openly that they set a higher price for some foreign customers. These were mostly younger sellers with less experience, who probably did care less about reputation effects.
- 68. 54 CHAPTER 9. THE FIELD RESEARCH Gender A customer’s gender has the second lowest mean of all the surveyed characteristics and the median is a straight 1. Over 73% of all respondents rated it 5 or lower. There are no differences in the results on the second level, and only the leather sellers who are also store owners delivered uncertain results. This can be explained that a big part of their product spectrum are leather purses and it seems obvious that men are not ready to pay as much as women for those items. Only a lack of experience could explain why their answers are such different from employees in the same sector. However, some merchants regardless of their sector claimed that, in general, women are better negotiators and often achieve to agree on lower prices than men. Showing Interest This feature is clearly one of the most important. It has a high mean and even a higher median. This makes intuitively sense since being very interested in a product automatically reveals that the buyer values it at a high degree. Over 56% of all answers were 6 or above for this feature. Nevertheless, there are peaks on each end of its histogram. On the second level, the data displays that showing interest does not matter for carpet dealers, and so it is for approximately half of the textile and gift sellers. However, the jewellers and leather sellers seem to be sensitive to such behaviour and would let the price get affected by showing interest. There is also a big difference between owners and employees. Employees will try to get more out of negotiations with an interested buyer. On the third level, more or less the same results are observable with the one exception that the employees of jewellery stores caused the outcome on the second level, the owners gave moderate answers.
- 69. 9.2. RESULTS 55 Wearing Apparel This buyer’s feature has very balanced4 results on the ﬁrst level. 53% of all responses were a 5 or below. On the second level, the results are balanced as well, except for carpet sellers who seem not to care how the wearing apparel of their customers are, on the contrary, leather sellers in general care a lot. On the third level, we can add the employees of gift shops to the group of leather sellers. It must be noted that the employees of gift shops gave high answers in general. This can be explained with their age. 74% of the sellers are under 35 years old, whereas the share of merchants under 35 is at 43% in the surveyed population. Accent A customer’s accent was through all levels and all clusters unimportant, except for employees of gift shops. Their answers were balanced. The same is observable in the second section of the questionnaire in which over 80% of the interviewees did not agree with the statement that an accent-free speaking of Turkish lowers the price. Sympathy This characteristic has the second highest mean and the highest median. It seems not rational for sellers to let themselves inﬂuence by sympathy, but 63% of all answers were 6 or higher. Only carpet dealers and the textile sellers delivered balanced results in their answers. All other clusters set their initial price lower if their customer is pleasant. This extreme results are caused by the employees, who are much more affected by this characteristic. The shop owners gave balanced answers. Number of Articles This is the characteristic which has the highest mean and median. Almost 72% of all the answers were 6 or above in the ﬁrst section of the question- 4Balanced means in this context that peaks appear on both sides of the histogram.
- 70. 56 CHAPTER 9. THE FIELD RESEARCH naire. The results are even higher in the second section in which over 81% agreed or strongly agreed that a higher quantity reduces the price. This result was expected, since in the western civilisations a quantity discount is common practice as well. The results look the same on each level, only the jewellery shop owners gave balanced answers to this question. The quantity discount seems to lose a part of its effect when it comes to really expensive goods. Time of the Day This is one feature on which all the different groups had the same opinion in general. The time does not seem to matter a lot. Although almost 19% of all merchants said that prices decrease when closing time comes closer, in order to increase the daily proﬁts. Many had the opinion that on the contrary they would charge a higher price for their goods because their customers would not have enough time to walk around and look for cheaper alternatives anymore. It would be also likely that a customer trying to buy something at such a late hour must be desperate and would therefore lose his bargaining power. The prior belief that late shopping gives buyers an advantage proved to be a myth. Nevertheless, it must be noted that a majority of the sellers believe in siftah. This Turkish word means the ﬁrst sell of the day. They plead that the ﬁrst sell of the day is the hardest and business starts running faster after it. This means that they are ready to agree on a rather low price early in the morning, some of them even on a price with a margin equal to zero. This only proves that most of the sellers at the Bazaar are superstitious at some degree and sometimes act irrational. Date The results from the ﬁrst section show that off-season some sellers decrease their prices, but in general the date does not have a big impact on the price. Nevertheless, merchants who were interviewed for a longer period of time, explained that in this particular year in which customers were
- 71. 9.2. RESULTS 57 rare, they even sell products for their production costs, in order to reduce their stocks and gain some liquidity for their business. Moreover, it is possible that there was a misunderstanding in the ﬁrst section. In the second question of the questionnaire, in which off-season was particularly mentioned, over 45% of the sellers answered that they lower their prices off-season. Wanting a Receipt Based on a well known problem in Turkey, buyers often get discounts if they waive to get a receipt after a purchase. No receipt means no taxes and the decrease in future losses can be split between buyer and seller. However, the results display that this must have changed in Turkey over the last decade, at least in the Grand Bazaar. This feature has the lowest mean and median and over 82% of all merchants gave an answer of 5 or below. Paying in Cash The results for this parameter look balanced on the ﬁrst level, although this changes one level deeper. For the gift and textile sector it is more important that their customers pay in cash than in the others. This can easily be explained by the transactional fees the credit card companies charge the stores. This fees are charged for every transaction and typically consist of a percentage of each transaction accompanied by a ﬂat per transaction fee. The ﬁrst part in which a percentage of the purchase is charged applies to all stores but the second part is for gift and textile sellers higher in proportion to the prices they charge for their goods then for a jeweller. Other Characteristics There were only 13 sellers who actually used the blank spaces to add char- acteristics they thought were important. 5 of the 13 interviewees wrote that
- 72. 58 CHAPTER 9. THE FIELD RESEARCH Table 3: Correlation Matrix min max range discount age 0.157 0.145 0.102 0.129 nationality 0.217 0.264 0.220 0.325 gender −0.005 0.044 0.056 0.106 interest 0.100 0.178 0.170 0.277 wearing 0.127 0.220 0.208 0.327 accent 0.150 0.230 0.211 0.330 sympathy 0.106 0.131 0.110 0.240 number 0.088 0.184 0.183 0.227 time 0.130 0.198 0.181 0.288 date 0.007 0.138 0.165 0.286 receipt −0.028 −0.049 −0.047 0.112 cash 0.011 −0.070 −0.091 0.231 min 1 0.618 0.283 0.338 max 0.618 1 0.929 0.465 range 0.283 0.929 1 0.409 discount 0.338 0.465 0.409 1 being a regular customer and/or coming to the shop by recommendation affects the price a lot. This gives a hint that reputation effects are present in the Grand Bazaar. The following three features can be summarised into one category, the merchants said that the customer should be respectful, serious and under no circumstances behave like a "smarty pants". These three features will affect the price negatively if the seller is not pleased with a buyer’s behaviour. They all relate to the characteristic "sympathy". For 4 of the sellers a buyer’s profession is an important feature. For instance, if a buyer is a merchant himself then the price will probably be affected by this. Last but not least, experience was mentioned by the sellers. A buyer who has a lot of experience and knowledge in one sector will get lower prices.
- 73. 9.2. RESULTS 59 Table 4: Price range distribution Range ≥ Jewellery Carpet Textile Leather Gift 150% 5.26% 5.26% 3.70% 19.23% 19.15% 100% 7.02% 15.79% 3.70% 23.08% 27.66% 70% 10.53% 26.32% 11.11% 42.31% 36.17% 50% 17.54% 52.63% 37.04% 42.31% 55.32% 40% 19.30% 57.89% 40.74% 46.15% 63.83% 30% 29.82% 63.16% 48.15% 53.85% 76.60% 20% 52.63% 78.95% 59.26% 73.08% 80.85% 10% 77.19% 94.74% 66.67% 80.77% 89.36% Total 57 (100%) 19 (100%) 27 (100%) 26 (100%) 47 (100%) Table 5: Discount distribution Discount ≥ Jewellery Carpet Textile Leather Gift 50% 8.77% 10.53% 0% 7.69% 27.66% 40% 12.28% 21.05% 7.41% 15.38% 34.04% 30% 26.32% 31.58% 29.63% 50.00% 59.57% 20% 42.11% 52.63% 62.96% 84.62% 76.60% 10% 78.95% 94.74% 88.89% 96.15% 93.62% Total 57 (100%) 19 (100%) 27 (100%) 26 (100%) 47 (100%)
- 74. 60 CHAPTER 9. THE FIELD RESEARCH Range and Discount Consider table 3 in which the different correlations of buyer’s characteris- tics to price ranges5 and discount during negotiations are pictured. There is no remarkable correlation between any characteristic and any cost re- lated value (min, max, range, discount). From the price range distributions in table 4 it can be identiﬁed that especially leather and gift sellers have wide price ranges. Whereas this result is expected for gift sellers as a reason of very low production costs for some of their items, it is harder to justify the results for sellers of leather products, especially for the results above 70%. Although, gift and leather sellers have similar distributions in table 4, their distributions in table 5 differ a lot. Leather dealers are much more unlikely to give high discounts on their products. One of the leather sellers mentioned that he would not give a high discount even if he set the initial price extremely high above his costs. He would stick to his strategy and try to get a high proﬁt out of the deal. A discount which exceeds a certain amount does not always increase the probability of an agreement. At one point a potential buyer gets suspicious and asks himself how such a high discount is possible. He may even question a product’s quality or even the seller’s honesty which can easily lead to an abortion of negotiation. The jewellers have the tightest price ranges which is also an expected results, for the same reason as for gift sellers. Since their production costs are much higher, their price ranges vary a lot less in relation to their costs. It must be noted that at the 10% mark they get undercut by the textile sellers. The reason for that is, that there are a rising number of textile dealers who work with ﬁxed prices. They write prices on their goods, like fashion stores in Western countries do, which eliminates the price range. This does not mean that they do not negotiate at all, but they give lower discounts than other stores. The carpet sellers seem to have a great ﬂexibility in setting their prices regardless of their expensive products. 5The price range is the difference between what a seller would add max and min on top of his costs.
- 75. 9.3. IMPLICATIONS 61 Prices for carpets can vary a lot, especially if they are handmade and for a layman it is hard to determine their value. For this reason and for the uniqueness of handmade carpets, the carpet dealers gain more ﬂexibility in their price settings and in their range for negotiations. 9.3 Implications One of the purposes of this thesis was to ﬁnd important characteristics of a buyer to recommend an optimal strategy for those who want to go shopping at the Grand Bazaar of Istanbul. The optimal customer can be inferred from the results in the previous section. To make a seller believe that one has a very low reservation value and to ﬁnd an agreement on the lowest possible price6, a buyer should fulﬁl following characteristics or should send someone instead who does. • The ideal customer should be a young, local student. • He should desist from showing interest in the desired product. • He should wear cheap clothes. • He must ﬁnd a way to bond with the seller so that he likes him. In order to achieve that, he must act serious and respectful and he must reveal his knowledge about the sector and its goods without sounding like a "smarty pants". • He should concentrate on buying goods off-season and visit the Bazaar as early in the morning as possible to beneﬁt from from the seller’s superstition of "siftah". • If it is possible, he should buy as many items as possible from one and the same store and should return to the same store again every time he needs similar items. This way he will gain a status as a regular and proﬁt from lower prices. 6Idealy at the sellers reservation value.