博弈论( GAME THEORY) LECTURE 1 TomH.Luan(栾浩) tom.luan@xidian.edu.cn CES, Xidian University
博弈论 （GAME THEORY） LECTURE 1 Tom H. Luan （栾浩） tom.luan@xidian.edu.cn CES, Xidian University
Outline of static games of complete Information ■ ntroduction to games Normal-form(or strategic-form) representation a Iterated elimination of strictly dominated strategIes Nash equilibrium Applications of Nash equilibrium ■M× ed strategy Nash equilibrium
4 Outline of Static Games of Complete Information ◼ Introduction to games ◼ Normal-form (or strategic-form) representation ◼ Iterated elimination of strictly dominated strategies ◼ Nash equilibrium ◼ Applications of Nash equilibrium ◼ Mixed strategy Nash equilibrium
什么是博弈论? 什么是博弈?任何需要顾及到个体利益的决策过程,都是博弈 ■博弈的特点 ■分布式:一般没有中央控制单元,博弈者各自为政 多成员:至少包含两名或以上博弈者 相互联系:一名博弈者的决定,可能会影响其他博弈者 ■对完整博弈过程的一种逻辑的分析 ■博弈过程:如大国博弈(贸易出口),或个人博弈(股票投资 种逻辑:没个博弈者( Game Player)都是理性的获取其最 大利益 ■分析: 如何制定博弈规则,从而形成最佳的系统(如联合国机制)? 每个博弈者,应当如何制定对其最优的策略,从而最大化其收益?
什么是博弈论？ ◼ 什么是博弈？任何需要顾及到个体利益的决策过程，都是博弈 ◼ 博弈的特点： ◼ 分布式：一般没有中央控制单元，博弈者各自为政 ◼ 多成员：至少包含两名或以上博弈者 ◼ 相互联系：一名博弈者的决定，可能会影响其他博弈者 ◼ 对完整博弈过程的一种逻辑的分析 ◼ 博弈过程：如大国博弈（贸易出口），或个人博弈（股票投资 ） ◼ 一种逻辑：没个博弈者（Game Player）都是理性的获取其最 大利益 ◼ 分析： ◼ 如何制定博弈规则，从而形成最佳的系统（如联合国机制）？ ◼ 每个博弈者，应当如何制定对其最优的策略，从而最大化其收益？ 5
稳定是关键! ■什么是博弈?任何需要顾及到个体利益的决策过程, 都是博弈 ■博弈的特点: ■分布式:一般没有中央控制单元,博弈者各自为政 多成员:至少包含两名或以上博弈者 ■相互联系:一名博弈者的决定,可能会影响其他博弈者 ■基础是稳定(纳什均衡( Nash equilibrium)) ■目标是利益最大化( Pareto Optimal)
稳定是关键！ ◼ 什么是博弈？任何需要顾及到个体利益的决策过程， 都是博弈 ◼ 博弈的特点： ◼ 分布式：一般没有中央控制单元，博弈者各自为政 ◼ 多成员：至少包含两名或以上博弈者 ◼ 相互联系：一名博弈者的决定，可能会影响其他博弈者 ◼ 基础是稳定（纳什均衡（Nash Equilibrium）） ◼ 目标是利益最大化（ Pareto Optimal ） 6
What is game theory We focus on games where There are at least two rational players Each player has more than one choices The outcome depends on the strategies chosen by all players; there is strategic interaction Strategic externality EXample: Six people go to a restaurant Each person pays his/her own meal -a simple decision problem Before the meal, every person agrees to split the bill evenly among them-a game
7 What is game theory? ◼ We focus on games where: ➢ There are at least two rational players ➢ Each player has more than one choices ➢ The outcome depends on the strategies chosen by all players; there is strategic interaction ➢ Strategic externality ◼ Example: Six people go to a restaurant. ➢ Each person pays his/her own meal – a simple decision problem ➢ Before the meal, every person agrees to split the bill evenly among them – a game
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