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1、Chapter 1 完全信息静态博弈 Static Games of Complete Information,In this chapter we consider games of the following simple form: first, the players simultaneously choose actions; then, the players receive payoffs that depend on the combination of actions just chosen. Within the class of such static (or simul
2、taneous-move) games,we restrict attention to games of complete information. That,is each players payoff function (the function that determines the players payoff from the combination of actions chosen by the players) is common knowledge among all the players. 教材P21,一、Normal-Form Representation of Ga
3、mes and Nash Equilibrium,(一)Normal-Form Representation of Games,In the normal-form representation of a game ,each player simultaneously chooses a strategy, and the combination of strategies chosen by the players determines a payoff for each player. We illustrate the normal-form representation with a
4、 classical exampleThe prisoners Dilemma.,Two suspects are arrested and charged with a crime. The police lack sufficient evidence to convict the suspects, unless at least one confesses.The police hold the suspects in separate cells and explain the consequences,that will follow from the actions they c
5、ould take. If neither confesses then both will be convicted of a minor offense and sentenced to one year in jail. If both confess then both will be sentenced to jail five years. Finally, if one confesses but the other does not, then the confessor will be released immediately but the other will be se
6、ntenced to eight years in jailfive for the crime and a further three for obstructing justice(干扰司法)。,囚徒 招认 沉默 招认 5, -5 0, -8 囚徒 沉默 -8, 0 -1 , -1 囚徒的困境,We now turn to the general case. The normal-form representation of a game specifies: (1)the players in the game;(2)the strategies available to each pl
7、ayer;(3)the payoff received by each player for each combination of strategies that could be chosen by the players.,Definition: The normal-form representation of an-n-player game specifies the players strategy spaces S1 , , Sn and their payoff functions u1 , un. We denote this game by G=S1, ,Sn;u1, ,
8、 un. 教材 22,理解完全信息静态博弈时要注意事项, Although we stated that in a normal-form game the players choose their strategies simultaneously , this does not imply that the parties necessarily act simultaneously :it suffices that each choose his or her action without knowledge of the others choices, as would be the
9、 case “the prisonersdilemma” if the prisoners reached decisions at arbitrary times (在任意时间)while in their separate cells.,2 Here we may recognize complete information as that each player know the payoff functions of the others.,(二)Dominant-Strategy Equilibrium,Definition In the normal-form game G=S1,
10、 , Sn; u1, , un,let si and si“ be feasible strategies for player i (i.e., si and si“ are members of Si ). Strategy si is strictly dominated by strategy si“ if for each feasible combination of the others strategies, is payoff from playing si is strictly less than is payoff from playing si“ . i.e.:,ui
11、(s1, , si-1, si* , si+1 , , sn ) ui(s1, , si-1, si* , si+1 , , sn ) (DS) for each s-i= (s1, , si-1 , si+1 , , sn ) that can be constructed from the other playersstrategy Spaces S1, , Si-1, Si+1, Sn.,WATSON P55 1,囚徒 招认 沉默 招认 5, -5 0, -8 囚徒 沉默 -8, 0 -1 , -1 囚徒的困境,策略“沉默”严格劣于策略“招认”,博弈分析的目的：预测博弈的均衡结果， 即给
12、定“每个参与人都是理性的”是共同知识，什么是每个参与人的最优策略？什么是所有参与人的最优策略组合？,*肯定性（sure-thing）或替代性（substitution） 公理：一个决策者在事件发生的偏好选项 胜于选项，并且在事件不发生时也 偏好选项胜于选项，那么就有，他 在知道事件无论是发生还是不发生之 前都应该偏好选项胜于选项。,“理性的参与人不会选择严格劣策略”,俗语：已不变应万变,“重复剔除严格劣策略（iterated elimination of strictly dominated strategies）”的思路： 首先，找出某个参与人的严格劣策略，并 把它从他的策略空间中剔除，重新
13、构造一个已 不包含该严格劣策略的博弈； 其次，剔除新博弈中某个参与人的严格劣 策略； 重复上述过程，直到只剩下唯一的策略组 合。 我们认为这个唯一所剩的策略组合是稳定 的。 ,Definition In a normal-form game,if for each player i , si“ is is dominant strategy,than we call the strategies profile (s1, , sn“ ) the dominant- strategy equilibrium.,参与人 左 中 右 上 1，0 1，2 0，1 参与人 下 0，3 0，1 2，0,策
14、略组合（上，中）是均衡结局，将实现支付 （1，2）。,第一,第二,第三,参与人 左 中 右 上 , 4, 0 5, 3 参与人 中 4, 0 0, 4 5, 3 下 3, 5 3, 5 6, 6,每个参与人都不存在严格劣策略,（三）纳什均衡 Definition In the n-player normal-form game G=S1, , Sn; u1, , un, the strategies( s1*, sn* ) are a Nash equilibrium if,for each player i, si* is (at least tied for （至少不劣于）) player
15、 is best response to the strategies specified for the n-1 other players, ( s1*, sn-1* , sn+1* , sn* ): ui( s1*, sn-1* , si* , sn+1* , sn* ) ui( s1*, sn-1* , si , sn+1* , sn* ) .(NE),for every feasible strategy si in Si; That is , si*solves max ui( s1*, sn-1* , si, sn+1* , sn* ). siSi 上述均衡概念是1951年由数学家约翰纳什 （John Nash）首先解释清楚的，所以将他所解释的均衡称为纳什均衡。,*对纳什均衡的理解：,1 If game theory is to provide a unique solution to a game-theoretic problem then the solution must be a Nash equilibrium, in the following sense.Suppose that game theory makes a unique prediction about the strategy each player will c
