GAME THEORY MILOŠ FIŠAR course BPV_APEC Public Economics - 29/9/2015 WHEN DO WE PLAY A GAME? Decide what is a game or not: •Driver maneuvering in a heavy traffic. •Bargain-hunters bidding on eBay. •A firm and a union negotiating next year’s wage. •Candidates choosing their platforms in an election. •The owner of a grocery store deciding today’s price for corn flakes. A GAME IS BEING PLAYED WHENEVER HUMAN BEINGS INTERACT. driving game auctioning game bargaining game political game economic game GAME THEORY APPLICATION •Game theory might be applied to predict how people play any game of social life. •But game theory can’t solve all of the world problems. • •Game theory only works when people play rationally. THE THEORY OF RATIONAL CHOICE LET’S PLAY SOME GAMES •Matching Pennies •Prisoner’s Dilemma •Battle of the Sexes NASH EQUILIBRIUM •Occurs when all players are simultaneously making a best reply to the strategy choices of the others. • • MATCHING PENNIES Alice and Bob each show a coin. Alice wins if both coins show the same face. Bob wins if they show different faces. TRADITIONAL PRISONER’S DILEMMA Alice and Bob are Gangsters in Chicago. The District Attorney knows that they are guilty of a major crime, but is unable to convict either unless one of the confesses. He offers each a following deal: •If you confess and your accomplice fails to confess, then you go free. •If you fail to confess but your accomplice confesses, then you will be convicted and sentenced to maximum term in jail (10 years). •If you both confess, then you will both be convicted, but the maximum sentence will not be imposed (9 years). •If neither confesses, you will both be framed on a tax evasion for which conviction is certain (1 year). TRADITIONAL PRISONER’S DILEMMA UPGRADED PRISONER’S DILEMMA Alice and Bob have access to a pot of money. Both are independently allowed to give their opponent $2 from the pot, or put $1 into their pocket. NASH EQUILIBRIA OF PRISONER’S DILEMMA GAME BATTLE OF THE SEXES BATTLE OF THE SEXES BATTLE OF THE SEXES WHAT TYPES OF GAMES THERE ARE? •Cooperative/Non-cooperative •Symmetric / Asymmetric •Zero-sum / Non-zero-sum •Simultaneous / Sequential •Perfect information / imperfect information •Discrete and continuous games •Infinitely long games • GAMES •Matching Pennies •simple game, no Nash equilibria • •Prisoner’s Dilemma •cooperation game, strong Nash equilibria • •Battle of the Sexes •coordination game, two pure (but unfair) Nash equilibria I hope you know the answer J WHY TO USE GAME THEORY? LITERATURE •Binmore, Ken. Game theory: a very short introduction. Oxford University Press, 2007. •Binmore, Ken. Playing for Real Coursepack Edition: A Text on Game Theory. Oxford University Press, 2012. •Osborne, Martin J. An introduction to game theory. Vol. 3. No. 3. New York: Oxford University Press, 2004.