There is a set of participants, whom we call the players. In our example, you and yourpartner are the two players.(ii) Each player has a set of options for how to behave; we will refer to these as the player'spossible strategies. In the example, you and your partner each have two possiblestrategies: to prepare for the presentation, or to study for the exam.(iii) For each choice of strategies, each player receives a payo that can depend on thestrategies selected by everyone. The payos will generally be numbers, with eachplayer preferring larger payos to smaller payos. In our current example, the payoto each player is the average grade he or she gets on the exam and the presentation
Transcript of "Game Theory: an Introduction"
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DATA MINING AND MACHINE LEARNING IN A NUTSHELL GAME THEORY, AN INTRODUCTION Mohammad-Ali Abbasi http://www.public.asu.edu/~mabbasi2/ SCHOOL OF COMPUTING, INFORMATICS, AND DECISION SYSTEMS ENGINEERING ARIZONA STATE UNIVERSITY Arizona State University http://dmml.asu.edu/Data Mining and Machine Learning Lab Data Mining and Machine Learning- in a nutshell An Introduction to Game Theory 1
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Agenda • History • Introduction to Game Theory • Type of Games – Dominant Games – Nash Equilibrium – Multiple Equilibrium • Game Time Arizona State University Data Mining and Machine Learning Lab Data Mining and Machine Learning- in a nutshell An Introduction to Game Theory 2
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History • Interdisciplinary (Economic and Mathematic) approach to the study of human behavior • Founded in the 1920s by John von Neumann • 1994 Nobel prize in Economics awarded to three researchers • “Games” are a metaphor for wide range of human interactions Arizona State University Data Mining and Machine Learning Lab Data Mining and Machine Learning- in a nutshell An Introduction to Game Theory 3
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What is a Game • Game theory is concerned with situations in which decision-makers interact with one another, • and in which the happiness of each participant with the outcome depends not just on his or her own decisions but on the decisions made by everyone. Arizona State University Data Mining and Machine Learning Lab Data Mining and Machine Learning- in a nutshell An Introduction to Game Theory 4 4
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A Game! • Ten of you go to a restaurant • If each of you pays for your own meal… – This is a decision problem • If you all agree to split the bill... – Now, this is a game Arizona State University Data Mining and Machine Learning Lab Data Mining and Machine Learning- in a nutshell An Introduction to Game Theory 5
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Restaurant Decision-Making • Bill splitting policy changes incentives. May I recommend that with the Bleu Cheese for ten dollars more? Sure! It is only a dollar more for me! Arizona State University Data Mining and Machine Learning Lab Data Mining and Machine Learning- in a nutshell An Introduction to Game Theory 6
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Decision theory vs. Game theory • Decision Theory – You are self-interested and selfish • Game Theory – So is everyone else Arizona State University Data Mining and Machine Learning Lab Data Mining and Machine Learning- in a nutshell An Introduction to Game Theory 7 7
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Applications • Market: – pricing of a new product when other firms have similar new products – deciding how to bid in an auction • Networking: – choosing a route on the Internet or through a transportation networks • Politic: – Deciding whether to adopt an aggressive or a passive stance in international relations • Sport: – choosing how to target a soccer penalty kick and choosing how to defend against – Choosing whether to use performance-enhancing drugs in a professional sport Arizona State University Data Mining and Machine Learning Lab Data Mining and Machine Learning- in a nutshell An Introduction to Game Theory 8 8
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Introduction to Game Theory • Review a Game • Characteristics • Rules • Assumptions Arizona State UniversityData Mining and Machine Learning Lab Data Mining and Machine Learning- in a nutshell An Introduction to Game Theory 9
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The Prisoner’s Dilemma • Two burglars, Jack and Tom, are captured and separated by the police • Each has to choose whether or not to confess and implicate the other • If neither confesses, they both serve one year for carrying a concealed weapon • If each confesses and implicates the other, they both get 4 years • If one confesses and the other does not, the confessor goes free, and the other gets 8 years Arizona State University Data Mining and Machine Learning Lab Data Mining and Machine Learning- in a nutshell An Introduction to Game Theory 10
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Prisoners dilemma • Introduction Tom Not Confess Confess Not Confess -1, -1 -8, 0 Jack Confess 0, -8 -4, -4 Arizona State University Data Mining and Machine Learning Lab Data Mining and Machine Learning- in a nutshell An Introduction to Game Theory 11
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Jack’s Decision Tree If Tom Confesses If Tom Does Not Confess Jack Jack Confess Not Confess Confess Not Confess 4 Years in 8 Years in 1 Years in Free Prison Prison Prison Best Best Strategy Strategy Arizona State University Data Mining and Machine Learning Lab Data Mining and Machine Learning- in a nutshell An Introduction to Game Theory 12
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Basic elements of a Game • Players – Everyone who has an effect on your earnings • Strategies – Actions available to each player – Define a plan of action for every contingency • Payoffs – Numbers associated with each outcome – Reflect the interests of the players Arizona State University Data Mining and Machine Learning Lab Data Mining and Machine Learning- in a nutshell An Introduction to Game Theory 13
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Assumptions in the Game Theory • Player – We assume that each player knows everything about the structure of the game – Player don’t know about another’s decision – Each player knows the rules of the game – Players are rational and expert • Strategy – Each player has two or more well-specified choices – Each player chooses a strategy to maximize his own payoff – Every possible combination of strategies available to the players leads to a well-defined end-state (win, loss, draw) that terminates the game • Payoff – everything that a player cares about is summarized in the players payoffs Arizona State University Data Mining and Machine Learning Lab Data Mining and Machine Learning- in a nutshell An Introduction to Game Theory 14
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Basic Games • games with only two players – We can apply it on any number of players • simple, one-shot games – Simultaneously, Independent and only once – Not dynamic Arizona State University Data Mining and Machine Learning Lab Data Mining and Machine Learning- in a nutshell An Introduction to Game Theory 16
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Types of Games • Dominant Games • Nash Equilibrium • Multiple Equilibrium Arizona State UniversityData Mining and Machine Learning Lab Data Mining and Machine Learning- in a nutshell An Introduction to Game Theory 17
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Prisoner’s Dilemma If Tom Confesses If Tom Does Not Confess Jack Jack Confess Not Confess Confess Not Confess 4 Years in 8 Years in 1 Years in Free Prison Prison Prison Best Best Strategy Strategy Arizona State University Data Mining and Machine Learning Lab Data Mining and Machine Learning- in a nutshell An Introduction to Game Theory 18
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Dominant strategy • A players has a dominant strategy if that players best strategy does not depend on what other players do. P1(S,T) >= P1 (S’, T) • Strict Dominant strategy P1(S,T) > P1 (S’, T) • Games with dominant strategies are easy to play – No need for “what if …” thinking Arizona State University Data Mining and Machine Learning Lab Data Mining and Machine Learning- in a nutshell An Introduction to Game Theory 19
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Prisoners Dilemma • Strategies must be undertaken without the full knowledge of what other players will do. • Players adopt dominant strategies, • BUT they dont necessarily lead to the best outcome. Arizona State University Data Mining and Machine Learning Lab Data Mining and Machine Learning- in a nutshell An Introduction to Game Theory 20
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If only one player has Strictly dominant Strategy • Players: Firm A and Firm B – Produce a new product • Options: Low Price and Upscale • 60% of people would prefer low price and 40% high price • Firm A is dominant and can gets 80% of market Arizona State University Data Mining and Machine Learning Lab Data Mining and Machine Learning- in a nutshell An Introduction to Game Theory 21
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Marketing Strategy • Dominant Games Firm B Low Price Upscale Low .48, .12 .6, .4 Price Firm A Upscale .4, .6 .32, .08 Arizona State University Data Mining and Machine Learning Lab Data Mining and Machine Learning- in a nutshell An Introduction to Game Theory 22
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A three client Game • Two Firms: Firm 1 and Firm 2 • Three Clients: Client A, B and C • Conditions: – If two firms apply for same client can get half of its business – Firm 1 is too small to attract a business -> payoff = 0 – If firm 2 approaches to B or C on its own, it will take all their business (their business is worth 2) – A is larger client and its business is worth 8. they can work with it if both of them target it. Arizona State University Data Mining and Machine Learning Lab Data Mining and Machine Learning- in a nutshell An Introduction to Game Theory 23
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Marketing Strategy • Nash Equilibrium Firm 2 A B C A 4, 4 0, 2 0, 2 Firm 1 B 0, 0 1, 1 0, 2 C 0, 0 0, 2 1, 1 Arizona State University Data Mining and Machine Learning Lab Data Mining and Machine Learning- in a nutshell An Introduction to Game Theory 24
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Nash Equilibrium • A Nash equilibrium is a situation in which none of them have dominant Strategy and each player makes his or her best response – (S, T) is Nash equilibrium if S is the best strategy to T and T is the best strategy to S • John Nash shared the 1994 Nobel prize in Economic for developing this idea! Arizona State University Data Mining and Machine Learning Lab Data Mining and Machine Learning- in a nutshell An Introduction to Game Theory 25
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Multiple Equilibriums • Coordination Game • The Hawk-Dove Game Arizona State UniversityData Mining and Machine Learning Lab Data Mining and Machine Learning- in a nutshell An Introduction to Game Theory 26
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Coordination Game Your Partner Power Point Keynote Power 1, 1 0, 0 Point You Keynote 0, 0 1, 1 Arizona State University Data Mining and Machine Learning Lab Data Mining and Machine Learning- in a nutshell An Introduction to Game Theory 27
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Other samples of Coordination Game • Using Metric units of measurement of English Units • Two people trying to find each other in a crowded mall with two entrance • … • These games has more than one Nash Equilibrium Arizona State University Data Mining and Machine Learning Lab Data Mining and Machine Learning- in a nutshell An Introduction to Game Theory 28
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Unbalanced Coordination Game Your Partner Power Point Keynote Power 1, 1 0, 0 Point You Keynote 0, 0 2, 2 Arizona State University Data Mining and Machine Learning Lab Data Mining and Machine Learning- in a nutshell An Introduction to Game Theory 29
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Battle of the Sexes Wife Romantic Action Romantic 1, 2 0, 0 Husba nd Action 0, 0 2, 1 Arizona State University Data Mining and Machine Learning Lab Data Mining and Machine Learning- in a nutshell An Introduction to Game Theory 30
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Stag Hunt Game Hunter 2 Stag Hare Stag 4, 4 0, 3 Hunter 1 Hare 3, 0 3, 3 Arizona State University Data Mining and Machine Learning Lab Data Mining and Machine Learning- in a nutshell An Introduction to Game Theory 31
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Hawk- Dove game Animal 2 Dove Hawk Dove 3, 3 1, 5 Animal 1 Hawk 5, 1 0, 0 Arizona State University Data Mining and Machine Learning Lab Data Mining and Machine Learning- in a nutshell An Introduction to Game Theory 32
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Mixed Strategies- Matching Pennies Zero-sum Game Player 2 Head Tail Head -1, +1 +1, -1 Player 1 Tail +1, -1 -1, +1 Arizona State University Data Mining and Machine Learning Lab Data Mining and Machine Learning- in a nutshell An Introduction to Game Theory 33
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Be ready for a Game! Arizona State UniversityData Mining and Machine Learning Lab Data Mining and Machine Learning- in a nutshell An Introduction to Game Theory 34
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play a real game! • Select a random number between 0 and 100 • The winner is the one how, his number is closest to 0.75 of the average. – If average is AVG, closest number to AVG * 0.75 is winner • Score distribution: – 1st : 100 – 2nd : 50 – Others: 0 • Talk about your selection Arizona State University Data Mining and Machine Learning Lab Data Mining and Machine Learning- in a nutshell An Introduction to Game Theory 35
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Mohammad-Ali Abbasi (Ali), Ali, is a Ph.D student at Data Mining and Machine Learning Lab, Arizona State University. His research interests include Data Mining, Machine Learning, Social Computing, and Social Media Behavior Analysis. http://www.public.asu.edu/~mabbasi2/ Arizona State UniversityData Mining and Machine Learning Lab Data Mining and Machine Learning- in a nutshell An Introduction to Game Theory 36
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