第五讲 完美信息动态博弈.ppt

1、第五讲 Extensive games with perfect information,一、An example：entry game,The key features of a dynamic game of perfect information are that ：(a) the moves occur in sequence, (b) all previous moves are observed before the next move is chosen, and (c) the players payoffs form each feasible combination of

2、moves are common knowledge.,二、Strategies,在静态博弈中，博弈方一次性同时选择的行为就是博弈方的策略，这些策略的策略组合，以及所对应的各方得益，就是博弈的结果。 动态博弈方决策，不是博弈方在单个阶段的行为，而是各博弈方在整个博弈中轮到选择的每个阶段，针对前面阶段的各种情况作相应选择和行为的完整计划，以及由不同博弈方的这种计划构成的组合。动态博弈的结果包括双方（或多方）采用的策略组合，实现的博弈路径和各博弈方的得益。,二（1）Example 1,In entry game， the strategies is： Challenger：in，out Incum

3、bent：acquiesce，fight,二（2）Example 2,2,二（2）Example 2,Play 1 has two strategies：C and D； Play 2 has four strategies：EG，EH，FG，FH； And the outcome of the strategy pair (C,EG) and (C,EH) is (C,E)，.,二（3） Example 3,二（3） Example 3,Player 1 has four strategies：CG,CH,DG and DH (In particular, each strategy spe

4、cifies an action after the history (C,E) even if it specifies the action D at the beginning of the game, in which case the history (C,E) does not occur!) Player 2 has two strategies：E and F. The outcome of the strategy pair (DG,E) is the terminal history D, and the outcome of (CH,E) is the terminal

5、history (C,E,H).,三、Nash equilibrium,Definition (Nash equilibrium of extensive game with perfect information) The strategy profile s* in an extensive game with perfect information is a Nash equilibrium if，for every player i and every strategy ri of player i，the terminal history O(s*) generated by s*

6、is as least as good according to player is preferences as the terminal history O(ri, s*-i) generated by the strategy profile (ri, s *-i) in which player i chooses ri while every other player j chooses s*j. Equivalently, for each player i, for every strategy ri of player i, Where ui is a payoff funct

7、ion that represents player is preference and O is the outcome function of the game.,三（1） Example 1:The strategic form of the entry game and its Nash equilibrium,In the absence of the possibility of the incumbents making a commitment, we might think of its announcing at the start of the game that it

8、intends to fight; but such a threat is not credible, because after the challenger enters the incumbents only incentive is to acquiesce.,三（2） Example 2,三（3） Example 3,四、Commitment and credibility：example 1（开金矿博弈）,四、Commitment and credibility：example 2（有法律保障的开金矿博弈）,四、Commitment and credibility：example

9、 2（法律保障不足的开金矿博弈）,四、Conclusion,纳什均衡在动态博弈可能缺乏稳定性的根源，正是在于它不能排除博弈方策略中所包含的不可信的行为设定，也就是各种不可信的威胁和承诺。纳什均衡假定每一个参与人在选择自己的最优战略时假定所有其他参与人的战略选择是给定的，就是说，参与人并不考虑自己的选择对其他人选择的影响。由于这个原因，纳什均衡很难说是动态博弈的一个合理解，因为在动态博弈中，参与人的行动有先有后，后行动者的选择空间依赖于前行动者的选择，前行动者在选择自己的战略时不可能不考虑自己的选择对后行动者选择的影响。,五、Subgame and subgame perfect equilib

10、rium,定义（子博弈）：由一个动态博弈第一阶段以外的某阶段开始的后续博弈阶段构成的，有初始信息集和进行博弈所需要的全部信息，能够自成一个博弈的原博弈的一部分，称为原动态博弈的一个“子博弈”。 原博弈也是其本身的一个子博弈。,五（1）Subgame: example 1,五（1）Subgame: example 2,E,F,2，1,3，0,2,E,F,2，1,3，0,2,五（1）Subgame: example 3,E,F,3，1,1,2,0，0,1，2,G,H,1,五（2）Subgame perfect equilibrium,定义（子博弈完美纳什均衡）：如果在一个完美信息的动态博弈中，各博

11、弈方的策略构成的一个策略组合满足，在整个动态博弈及它的所有子博弈中都构成纳什均衡，那么这个策略组合称为该动态博弈的一个“子博弈完美纳什均衡”。 Every subgame perfect equilibrium is a Nash equilibrium. A subgame perfect equilibrium is a strategy profile that induces a Nash equilibrium in every subgame.,六、Finding subgame perfect equilibria of finite horizon games: backwar

12、d inductionexample 1,Challenger,Out,1，2,In,Incumbent,Acquiesce,Fight,2，1,0，0,The procedure of backward induction in this game yields the strategy pair (in, acquiesce).,六（2） example 2,G,H,2,The procedure of backward induction in this game yields the strategy pair (C, EH).,六（3） example 3,1,D,C,2,2，0,E

13、,F,3，1,1,0，0,1，2,G,H,The procedure of backward induction in this game yields the strategy pair (DG, E).,六（4）example 4,1,D,C,2,E,F,3，0,1，0,2，2,1，3,1，1,2，1,G,H,I,J,K,2,2,1,0,D,1,0,D,1,0,1,0,D,1,0,1,0,The procedure of backward induction yields the strategy pairs: (C,FHK), (C,FIK), (C,GHK), (D,GHK), (E,

14、GHK), and (D,GIK).,Two propositions,Proposition 1:(Subgame perfect equilibrium of finite horizon games and backward induction) The set of subgame perfect equilibria of a finite horizon extensive with perfect information is equal to the set of strategy profiles isolated by the procedure of backward induction. Proposition 2:(Existence of subgame perfect equilibrium) Every finite extensive game with perfect information