Game Theory Presentation

Abbas Keramati ( Assistant Professor) University of Tehran – MBA Fall 2008 Game Theory Quantitative Analysis for Decision Making M.Ghotbi M.Pajhouh Niya

Title ,[object Object],[object Object],DGDG Outline ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Title ,[object Object],[object Object],DGDG What is Game Theory? ,[object Object],[object Object]

Title ,[object Object],[object Object],DGDG History of Game Theory ,[object Object],[object Object],[object Object],[object Object],[object Object]

Title ,[object Object],[object Object],DGDG ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Applications of Game Theory

Title ,[object Object],[object Object],DGDG Key Elements of a game ,[object Object],[object Object],[object Object],[object Object],[object Object]

Title ,[object Object],[object Object],DGDG Types of games ,[object Object],[object Object],[object Object],[object Object],[object Object]

Title ,[object Object],[object Object],DGDG Pure Strategies ,[object Object],[object Object]

Title ,[object Object],[object Object],DGDG An Example: -12 7 -12 X2 7 6 Y2 6 7 10 Maximum 6 10 X1 Minimum Y1 A B

Title ,[object Object],[object Object],DGDG Mixed Strategies A mixed strategy game exists when there is no saddle point. Each player will then optimize their expected gain by determining the percent of time to use each strategy.

Title ,[object Object],[object Object],DGDG Nash Equilibrium (NE) A player’s best strategy is that strategy that maximizes that player’s payoff (utility), knowing the strategy's of the other players.

Title ,[object Object],[object Object],DGDG 2-players Zero-Sum games Player 1 Player 2 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],-1 , 1 1 , -1 1 , -1 -1 , 1 Tail Head Tail Head

Title ,[object Object],[object Object],DGDG Prisoner’s Dilemma ,[object Object],[object Object],[object Object],[object Object],[object Object]

Title ,[object Object],[object Object],DGDG Ted Confess Not Confess Confess Bill Not Confess Payoff Matrix for Prisoner’s Dilemma Both get 3 years 10 years for Bill 1 year for Ted 1 year for Bill 10 years for Ted Both get 5 years

Title ,[object Object],[object Object],DGDG An Example of Mixed Strategy game 0.5 0 A doesn’t bluff 0 B doesn’t believe 1 A bluffs B believes A B

Title ,[object Object],[object Object],DGDG Now let’s Play This Game Pirate Game A B D C E

Title ,[object Object],[object Object],DGDG Nash’s Equilibrium ,[object Object],[object Object],[object Object]

Title ,[object Object],[object Object],DGDG Definition: Nash Equilibrium Given others’ choices, player i cannot be better-off if she deviates from s i *

Title ,[object Object],[object Object],DGDG Nash’s Equilibrium cont.: Bayesian Nash Equilibrium ,[object Object],[object Object],[object Object],[object Object]

Title ,[object Object],[object Object],DGDG ,[object Object],[object Object],[object Object],[object Object],Refrences

Game Theory Presentation

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Game Theory Presentation