Data Mining and Machine Learning- in a nutshell Arizona State University Data Mining and Machine Learning Lab Arizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 1 D ATA M INING AND M ACHINE L EARNING IN A NUTSHELL G AME T HEORY, A N I NTRODUCTION Mohammad-Ali Abbasi S CHOOL OF C OMPUTING, I NFORMATICS, AND D ECISION S YSTEMS E NGINEERING A RIZONA S TATE U NIVERSITY

Data Mining and Machine Learning- in a nutshell Arizona State University Data Mining and Machine Learning Lab Arizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 2 Agenda History Introduction to Game Theory Type of Games – Dominant Games – Nash Equilibrium – Multiple Equilibrium Game Time

Data Mining and Machine Learning- in a nutshell Arizona State University Data Mining and Machine Learning Lab Arizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 3 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

Data Mining and Machine Learning- in a nutshell Arizona State University Data Mining and Machine Learning Lab Arizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 4 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. 4

Data Mining and Machine Learning- in a nutshell Arizona State University Data Mining and Machine Learning Lab Arizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 5 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 5

Data Mining and Machine Learning- in a nutshell Arizona State University Data Mining and Machine Learning Lab Arizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 6 Restaurant Decision-Making Bill splitting policy changes incentives. 6 May I recommend that with the Bleu Cheese for ten dollars more? Sure! It is only a dollar more for me!

Data Mining and Machine Learning- in a nutshell Arizona State University Data Mining and Machine Learning Lab Arizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 7 Decision theory vs. Game theory Decision Theory – You are self-interested and selfish Game Theory – So is everyone else 7

Data Mining and Machine Learning- in a nutshell Arizona State University Data Mining and Machine Learning Lab Arizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 8 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 8

Data Mining and Machine Learning- in a nutshell Arizona State University Data Mining and Machine Learning Lab Arizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 9 Review a Game Characteristics Rules Assumptions Introduction to Game Theory

Data Mining and Machine Learning- in a nutshell Arizona State University Data Mining and Machine Learning Lab Arizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 10 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

Data Mining and Machine Learning- in a nutshell Arizona State University Data Mining and Machine Learning Lab Arizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 11 Prisoners dilemma Introduction Tom Not Confess Confess Jack Not Confess -1, -1 -8, 0 Confess 0, -8-4, -4

Data Mining and Machine Learning- in a nutshell Arizona State University Data Mining and Machine Learning Lab Arizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 12 Jack’s Decision Tree

Data Mining and Machine Learning- in a nutshell Arizona State University Data Mining and Machine Learning Lab Arizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 13 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

Data Mining and Machine Learning- in a nutshell Arizona State University Data Mining and Machine Learning Lab Arizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 14 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 player's payoffs

Data Mining and Machine Learning- in a nutshell Arizona State University Data Mining and Machine Learning Lab Arizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 15 What makes games different? Timing of moves Are moves simultaneous or sequential? Nature of conflict and interaction Are players’ interests in conflict? Will players interact once or repeatedly? Informational conditions Are some players better informed? Enforceability of agreements Can contracts be enforced?

Data Mining and Machine Learning- in a nutshell Arizona State University Data Mining and Machine Learning Lab Arizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 16 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

Data Mining and Machine Learning- in a nutshell Arizona State University Data Mining and Machine Learning Lab Arizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 17 Dominant Games Nash Equilibrium Multiple Equilibrium Types of Games

Data Mining and Machine Learning- in a nutshell Arizona State University Data Mining and Machine Learning Lab Arizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 18 Prisoner’s Dilemma

Data Mining and Machine Learning- in a nutshell Arizona State University Data Mining and Machine Learning Lab Arizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 19 Dominant strategy A players has a dominant strategy if that player's 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

Data Mining and Machine Learning- in a nutshell Arizona State University Data Mining and Machine Learning Lab Arizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 20 Prisoner's Dilemma Strategies must be undertaken without the full knowledge of what other players will do. Players adopt dominant strategies, BUT they don't necessarily lead to the best outcome.

Data Mining and Machine Learning- in a nutshell Arizona State University Data Mining and Machine Learning Lab Arizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 21 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

Data Mining and Machine Learning- in a nutshell Arizona State University Data Mining and Machine Learning Lab Arizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 22 Marketing Strategy Dominant Games Firm B Low PriceUpscale Firm A Low Price.48,.12.6,.4 Upscale.4,.6.32,.08

Data Mining and Machine Learning- in a nutshell Arizona State University Data Mining and Machine Learning Lab Arizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 23 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.

Data Mining and Machine Learning- in a nutshell Arizona State University Data Mining and Machine Learning Lab Arizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 24 Marketing Strategy Nash Equilibrium Firm 2 ABC Firm 1 A 4, 40, 2 B 0, 01, 10, 2 C 0, 00, 21, 1

Data Mining and Machine Learning- in a nutshell Arizona State University Data Mining and Machine Learning Lab Arizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 25 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!

Data Mining and Machine Learning- in a nutshell Arizona State University Data Mining and Machine Learning Lab Arizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 26 Coordination Game The Hawk-Dove Game Multiple Equilibriums

Data Mining and Machine Learning- in a nutshell Arizona State University Data Mining and Machine Learning Lab Arizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 27 Coordination Game Your Partner Power PointKeynote You Power Point 1, 10, 0 Keynote 0, 01, 1

Data Mining and Machine Learning- in a nutshell Arizona State University Data Mining and Machine Learning Lab Arizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 28 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

Data Mining and Machine Learning- in a nutshell Arizona State University Data Mining and Machine Learning Lab Arizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 29 Unbalanced Coordination Game Your Partner Power PointKeynote You Power Point 1, 10, 0 Keynote 0, 02, 2

Data Mining and Machine Learning- in a nutshell Arizona State University Data Mining and Machine Learning Lab Arizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 30 Battle of the Sexes Wife RomanticAction Husba nd Romantic 1, 20, 0 Action 0, 02, 1

Data Mining and Machine Learning- in a nutshell Arizona State University Data Mining and Machine Learning Lab Arizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 31 Stag Hunt Game Hunter 2 StagHare Hunter 1 Stag 4, 40, 3 Hare 3, 03, 3

Data Mining and Machine Learning- in a nutshell Arizona State University Data Mining and Machine Learning Lab Arizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 32 Hawk- Dove game Animal 2 DoveHawk Animal 1 Dove 3, 31, 5 Hawk 5, 10, 0

Data Mining and Machine Learning- in a nutshell Arizona State University Data Mining and Machine Learning Lab Arizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 33 Mixed Strategies- Matching Pennies Zero-sum Game Player 2 HeadTail Player 1 Head -1, +1+1, -1 Tail +1, -1-1, +1

Data Mining and Machine Learning- in a nutshell Arizona State University Data Mining and Machine Learning Lab Arizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 34 Be ready for a Game!

Data Mining and Machine Learning- in a nutshell Arizona State University Data Mining and Machine Learning Lab Arizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 35 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: – 1 st : 100 – 2 nd : 50 – Others: 0 Talk about your selection

Data Mining and Machine Learning- in a nutshell Arizona State University Data Mining and Machine Learning Lab Arizona State University Data Mining and Machine Learning Lab An Introduction to Game Theory 36 Mohammad-Ali Abbasi (Ali), Ali, is a Ph.D student at Data Mining and Machine Learning Lab, Arizona State University.Data Mining and Machine Learning LabArizona State University His research interests include Data Mining, Machine Learning, Social Computing, and Social Media Behavior Analysis.