博弈论第四章素材.ppt

* Chapter 4 Static Games of Incomplete Information This chapter begins our study of games of incomplete information, also called Bayesian games. Recall that in a game of complete infor- mation the players’ payoff functions are common knowledge. In a game of incomplete information, in contrast, at least one player is uncertain about another player’payoff function. One common example of a static game of incomplete informa -tion is a sealed-bid auction: each bidder knows his or her own valuation for the good being sold but does not know any other bidder’s valuation; bids are submitted in sealed envelopes, so the players’ moves can be thought of as simultaneous. Most economically interesting Bayesian games, however, are dynamic. As we will see in Chapter 5, the existence of private information leads naturally to attempts by informed parties to com- municate(or mislead) and to attempts by unin- formed parties to learn and respond. This are inherently dynamic issues. 一、Theory: Static Bayesian Games and Bayesian Nash Equilibrium （一）An Example: Cournot Competition under Asymmetric Information … C1(q1)=Cq1 , common knowledge,but C2(q2)=? , firm 2’s private information Firm 2 knows its cost function and firm 1’s, but firm 1 only knows its cost function(does not know firm 2’s cost function). All of this is common knowledge. Firm 1 knows: firm 2’s cost function is C2(q2)= CHq2 with probability θ and C2(q2)= CLq2 with probability 1- θ, where CL ＜ CH. common knowledge q2*(CH) will solve [a-q1*-q2-cH] q2 q2 q2*(CH)= a - q1*- cH 2 max (1)式： q2*(CL) Will solve [a-q1*-q2-cL] q2 max q2 q2*(CL)= a - q1*- cL 2 q1* Will solve [a-q1-q2*(CL)-c] q1 [a-q1-q2*(CH)-c] q1 (1-θ) θ + { } max q1 （2）式： q1* = (1- θ)[a-q2*(CL)-c]+ θ [a-q2*(CH)-c] 2 （3）式 The solutions to ?1 ,?2 and ?3 are q2*(CH)=(a-2CH+C)/3 + (1- θ)(CH – Cl )/6 q2*(CL)= (a-2CL+C)/3 – θ(CH – Cl )/6 q1* =[a-2C+ θCH +(1- θ)CL ]/3 不完全信息下古诺竞争的贝叶斯NE ?与完全信息下古诺竞争的NE作比较： 令a=8，C=2，CH=3， C