Ultimatum
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1. The ultimatum game involves two players dividing a fixed amount, with the first player proposing a division and the second deciding to accept or reject. 2. Early experiments found people offered more, around 40-50% of the amount, inconsistent with the rational prediction of minimal offers being accepted. 3. Further experiments explored factors like fairness, rejection fears, and information in bargaining, finding both explanations valid and information promoting fairness.
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s to Problem Set 2
The following note was very important for the solutions:
In all problems below a rational preference relation is understood as one that satisfies the axioms of
von Neumann and Morgenstern’s utility theory. When solving these problems involving the
expected utility theory use the von Neumann-Morgenstern theorem. In other words, you prove that
a preference relation is rational by showing utility values that satisfy corresponding conditions and
you prove that a preference relation is not rational by showing that no utility values can possibly
satisfy these conditions. SOLUTIONS THAT DON’T USE THIS METHOD WILL NOT BE
ACCEPTED !!!
Problem 1 (3p) Suppose you have asked your friend Peter if he prefers a sure payment of
$20 or a lottery in which he gets $15 with probability 0.5 and $10 with probability 0.5. Is it
rational for Peter to prefer the sure payment over the lottery? Is it rational to prefer the
lottery over the sure payment? Is it rational to be indifferent between the lottery and the sure
payment? Would your answer be any different had I asked you the same question but with
A substituted for $20, B for $15 and C for $10? What is the general lesson to learn from
this exercise?
SOLUTION: You can assign numbers to u($20), u($15) and u($10) in such a way that
u($20) will be larger than, or equal to, or smaller than 0.5u($15)+0.5u($10). This shows that
all three preferences are rational. If instead of $20, $15 and $10 you write A, B and C the
solution to this problem, which does not depend in any way on the specifics of the three
alternatives, should be obvious. A few general lessons here: (1) Expected utility theory,
just like preference theory, does not “impose any values” on your preferences. (2) Be
careful never to use assumptions that are not clearly stated. (3) If you are given a single
piece of information about decision maker’s preferences then no matter what this
information is it cannot be possibly irrational. Rationality is, in essence, a requirement of
consistency of preferences. If there is only one condition, what would it be possibly
inconsistent with?
Problem 2 (3p) George tells you that he prefers more money over less. George also tells
you about his preference between a lottery in which he gets $30 with probability 0.9 and 0
with probability 0.1 and a sure payment of $20. Assume that George is rational. Is it
possible for him to prefer the lottery over the sure payment? Is it possible to prefer the sure
payment over the lottery? Is it possible for him to be indifferent between the sure payment
and the lottery? What is the general lesson to learn from this exercise?
SOLUTION: Suppose you have assigned numbers to u($30), u($20) and u($0) in such a
way that u($30)>u($20)>u($0):
Can such numbers satisfy u($20) < 0.9u($30)+0.1u($0)? Yes, they can. For instance,
u($30)=1, u($20)=0.5 and u($0)=0. .
Risk and Rationality: Decision Making in the Brain
The document summarizes research on decision-making and risk-taking from both economic and neuroscience perspectives. Key findings include:
- Prospect theory shows people are generally risk-averse for gains and risk-seeking for losses. Animal studies also found different risk preferences.
- EEG studies identified ERP components like FRN, P300, and N500 that reflect outcome evaluation and risk-taking. FRN was larger for losses while P300 amplitude varied with motivational factors.
- Context affects risk preferences - people took more risks in contexts with positive expected value compared to zero or negative expected value. FRN and P300 reflected these context effects.
Documento CERAC No. 1: It's not how you play the game, it's winning that matt...
Documento CERAC No. 1: It's not how you play the game, it's winning that matt...CERAC - Centro de Recursos para el Análisis de Conflictos
This paper reports an experimental test of asymmetric Tullock contests. Both the simultaneous-move and sequential-move frameworks are considered. The introduction of asymmetries in the contest function generates experimental behavior qualitatively consistent with the theoretical predictions. However, especially in the simultaneous-move framework, average bidding levels are in excess of the risk-neutral predictions. We conjecture that the reason behind this behavior lies in subjects attaching positive utility to victory in the contest. Game theory
This document provides an overview of game theory concepts including its development, assumptions, classification of games, elements, significance, limitations, and methods for solving different types of games. Some key points:
- Game theory was developed in 1928 by John Von Neumann and Oscar Morgenstern to analyze decision-making involving two or more rational opponents.
- Games can be classified as two-person, n-person, zero-sum, non-zero-sum, pure-strategy, or mixed-strategy.
- Elements include the payoff matrix, dominance rules, optimal strategies, and the value of the game.
- Methods for solving games include using pure strategies if a saddle point exists, or mixed
Lecture OverviewSolving the prisoner’s dilemmaInstrumental r.docx
Lecture Overview
Solving the prisoner’s dilemma
Instrumental rationality
Morality & norms
Repeated games
Three ways to solve the prisoner’s dilemma
Sequential games
Backward induction
Subgame perfect Nash equilibrium
Common knowledge of rationality
Mixed strategies
Game theory: underlying assumptions
Remember:
Homo economicus: instrumental rationality and preferences
Common knowledge of rationality and consistent alignment of believes: given the same information individuals arrive at the same decisions
Individuals know the rules of the game which are exogenously given and independent of individuals’ choices
We will look at these one by one, analysing alternative assumptions.
We will use the prisoner’s dilemma as example.
Why?
Coordination game with conflict
Arguably it describes many social situations, e.g. the free rider problem:
Voting
Trade union affiliation
Wage cuts to increase profit
Domestic work
Prisoner’s dilemma
The homo economicus maximises his/her utility.
In a prisoner’s dilemma the dominant strategy is to confess (defect).
Fallacy of compositions: what is individually rational is neither Pareto optimal not socially rational.
But do people really defect?
Kant’s categorical imperative: not the outcome but the act is crucial (morality)
Altruism: blood donation
Social norms: forest people hunting in the Congo (Turnbull 1963)
Instrumental rationality
Gauthier: it is instrumentally rational to cooperate rather than to defect
Assume there are two sorts of maximisers in the economy: straight maximisers (SM) and constrained maximisers (CM); SMs defect, CMs cooperate with other CMs:
E(return from CM) = p*(-1)+(1-p)*(-3)
E(return from SM) = -3
For any p>0 the CM
strategy is better than
the SM one.
Instrumental rationality
Tit-for-tat
Unsurprisingly (maybe), in a repeated Prisoner’s dilemma the best strategy is not to defect but to adopt a tit-for-tat strategy.
In the 1980s, Robert Axelrod invited professional game theorists to enter strategies into a tournament of a repeated game (200 times).
The winning strategy was tit-for-tat entered by Anatol Rapaport:
Start off with cooperation
If opponent defects punish him/her by defecting
If opponent comes back to cooperation ‘forgive’ them and go back to cooperation
Overall, forgiving and cooperative strategies did better.
Repeated games & reputation
A tit-for-tat strategy can only be played in repeated games.
The folk theorem states that in an infinitely repeated game (or given uncertainty to the end of the game) any strategy with a feasible payoff can be an equilibrium.
This is important for social interaction: the prisoner’s dilemma can be overcome without (!) external authority.
Players enforce compliance (cooperate rather than defect) through punishment.
The loss of future returns deters players from defecting.
The surprising thing about Axelrod’s tournament was that the tit-for-tat strategy won in a finite (and defined) repeated game ...
9860380.ppt
Does any player have a dominated strategy?
If there is a dominated strategy, eliminate it.
If there is no dominant or dominated strategy, the game is unsolved by dominance. We need to look at other solution concepts like Nash equilibrium.
Digit ratio kobe_millet
The presence of aggression cues inverts the
relation between digit ratio (2D:4D) and prosocial behaviour in a dictator game
Ssrn a brief inrtoduction to the basic of game theory
1. The document provides a brief introduction to the basics of game theory, covering fundamental concepts such as normal form games, dominant strategies, and Nash equilibrium.
2. It uses the prisoners' dilemma game and a Cournot duopoly game to illustrate the concept of a normal form game and dominant strategies. Both games have a unique Nash equilibrium where both players defect.
3. Nash equilibrium is defined as a profile of strategies where each player's strategy is a best response to the other players' strategies. An example advertising game is presented to illustrate the concept of Nash equilibrium.
Game Theory_1.pptx
Game theory is a strategic decision-making process that models interactions between two or more players. It is commonly used in economics to analyze industries and competition between firms. Key concepts in game theory include games, players, strategies, payoffs, information sets, equilibriums, assumptions of rationality and payoff maximization. Common solution techniques include backwards induction, Nash equilibriums, mixed strategies, and minimax strategies. Examples discussed include prisoner's dilemmas, zero-sum games, and dominance.
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Evolutionary Ultimatum Game With Responders Dissatisfaction
Evolutionary Ultimatum Game With Responders Dissatisfaction
The analysis of sequential experiments with feedback to subjects
The analysis of sequential experiments with feedback to subjects
GAME THEORY NOTES FOR ECONOMICS HONOURS FOR ALL UNIVERSITIES BY SOURAV SIR'S ...
GAME THEORY NOTES FOR ECONOMICS HONOURS FOR ALL UNIVERSITIES BY SOURAV SIR'S ...
Solutions to Problem Set 2 The following note was very i.docx
Solutions to Problem Set 2 The following note was very i.docx
Risk and Rationality: Decision Making in the Brain
Risk and Rationality: Decision Making in the Brain
Documento CERAC No. 1: It's not how you play the game, it's winning that matt...
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Ultimatum
- 4. Analyzed data by Spiegel et al. (1994)
- 6. Experiment 1
- 7. Experiment 2
- 18. Having some information this time fairness dominates