a Beautiful mind ■约翰纳什,生于1928年6月13日。著名经济学家、博弈论创始人 ,因对博弈论和经济学产生了重大影响,而获得1994年诺贝尔经 济学奖。2015年5月23日,于美国新泽西州逝世 ■1950年于其仅27页的博士论文中提出重要发现,这就是后来被称 为“纳什均衡”的博弈理论 USSELL CROWE ED HARRIS A MINDL 1+h
A Beautiful Mind ◼ 约翰·纳什，生于1928年6月13日。著名经济学家、博弈论创始人 ，因对博弈论和经济学产生了重大影响，而获得1994年诺贝尔经 济学奖。2015年5月23日，于美国新泽西州逝世 ◼ 1950年于其仅27页的博士论文中提出重要发现，这就是后来被称 为“纳什均衡”的博弈理论 8
What is game theory Game theory is a formal way to analyze strategic interaction among a group of rational players(or agents) a Game theory has applications >Economics/Politics/Sociology /Law/Biology >The double helixand unifying tool for social scientists
9 What is game theory? ◼ Game theory is a formal way to analyze strategic interaction among a group of rational players (or agents) ◼ Game theory has applications ➢ Economics/Politics/Sociology/Law/Biology ➢ The “double helix” and unifying tool for social scientists
Classic Example: Prisoners Dilemma Two suspects held in separate cells are charged with a major crime. However, there is not enough evidence Both suspects are told the following policy If neither confesses then both will be convicted of a minor offense and sentenced to one month in jail If both confess then both will be sentenced to jail for six months y If one confesses but the other does not then the confessor will be released but the other will be sentenced to jail for nine months Prisoner 2 Mum Confess Mum 1 1-9 Prisoner 1 Confess 0 9|-6 6 10
10 Classic Example: Prisoners’ Dilemma ◼ Two suspects held in separate cells are charged with a major crime. However, there is not enough evidence. ◼ Both suspects are told the following policy: ➢ If neither confesses then both will be convicted of a minor offense and sentenced to one month in jail. ➢ If both confess then both will be sentenced to jail for six months. ➢ If one confesses but the other does not, then the confessor will be released but the other will be sentenced to jail for nine months. -1 , -1 -9 , 0 0 , -9 -6 , -6 Prisoner 1 Prisoner 2 Confess Mum Confess Mum
Example: The battle of the sexes At the separate workplaces, chris and pat must choose to attend either an opera or a prize fight in the evening Both Chris and Pat know the following Both would like to spend the evening together But Chris prefers the opera Pat prefers the prize fight ■Non- zero-sum game Opera Prize Fight Opera 1|0 0 Chris 20 Prize Fight 01 2
11 Example: The battle of the sexes ◼ At the separate workplaces, Chris and Pat must choose to attend either an opera or a prize fight in the evening. ◼ Both Chris and Pat know the following: ➢ Both would like to spend the evening together. ➢ But Chris prefers the opera. ➢ Pat prefers the prize fight. ◼ Non-zero-sum game 2 , 1 0 , 0 0 , 0 1 , 2 Chris Pat Prize Fight Opera Prize Fight Opera
Example: Matching pennies each of the two players has a penny Two players must simultaneously choose whether to show the head or the tail Both players know the following rules If two pennies match(both heads or both tails)then player 2 wins player 1's penny > Otherwise, player 1 wins player 2s penny Zero-sum game: no way for collaboration layer 2 Head Head 1 11 1 Player 1 Tail 1 1|-1 1
12 Example: Matching pennies ◼ Each of the two players has a penny. ◼ Two players must simultaneously choose whether to show the Head or the Tail. ◼ Both players know the following rules: ➢ If two pennies match (both heads or both tails) then player 2 wins player 1’s penny. ➢ Otherwise, player 1 wins player 2’s penny. ➢ Zero-sum game: no way for collaboration -1 , 1 1 , -1 1 , -1 -1 , 1 Player 1 Player 2 Tail Head Tail Head