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1、Static (or Simultaneous- Move) Games of Incomplete InformationIntroduction to Static Bayesian GamesJune 20, 2003173-347 Game Theory-Lecture 23Outline of Static Games of Incomplete Information nIntroduction to static games of incomplete informationnNormal-form (or strategic-form) representation of st
2、atic Bayesian gamesnBayesian Nash equilibriumnAuctionJune 20, 2003273-347 Game Theory-Lecture 23Todays AgendanReview of previous classnCournot duopoly model of incomplete information (version two)nBattle of sexes with incomplete information (version one)June 20, 2003373-347 Game Theory-Lecture 23Sta
3、tic (or simultaneous-move) games of complete informationnA set of players (at least two players) nFor each player, a set of strategies/actions nPayoffs received by each player for the combinations of the strategies, or for each player, preferences over the combinations of the strategiesnAll these ar
4、e common knowledge among all the players.June 20, 2003473-347 Game Theory-Lecture 23Static (or simultaneous-move) games of INCOMPLETE informationnPayoffs are no longer common knowledgenIncomplete information means that At least one player is uncertain about some other players payoff function.nStatic
5、 games of incomplete information are also called static Bayesian games June 20, 2003573-347 Game Theory-Lecture 23Cournot duopoly model of incomplete information (version one)nA homogeneous product is produced by only two firms: firm 1 and firm 2. The quantities are denoted by q1 and q2, respectivel
6、y. nThey choose their quantities simultaneously.nThe market price: P(Q)=a-Q, where a is a constant number and Q=q1+q2.nFirm 1s cost function: C1(q1)=cq1.nAll the above are common knowledgeJune 20, 2003673-347 Game Theory-Lecture 23Cournot duopoly model of incomplete information (version one) contdnF
7、irm 2s marginal cost depends on some factor (e.g. technology) that only firm 2 knows. Its marginal cost can be HIGH: cost function: C2(q2)=cHq2.LOW: cost function: C2(q2)=cLq2. nBefore production, firm 2 can observe the factor and know exactly which level of marginal cost is in. nHowever, firm 1 can
8、not know exactly firm 2s cost. Equivalently, it is uncertain about firm 2s payoff. nFirm 1 believes that firm 2s cost function isC2(q2)=cHq2 with probability , andC2(q2)=cLq2 with probability 1. nAll the above are common knowledgeJune 20, 2003773-347 Game Theory-Lecture 23Cournot duopoly model of in
9、complete information (version one) contdJune 20, 2003873-347 Game Theory-Lecture 23Cournot duopoly model of incomplete information (version two) nA homogeneous product is produced by only two firms: firm 1 and firm 2. The quantities are denoted by q1 and q2, respectively. nThey choose their quantiti
10、es simultaneously.nThe market price: P(Q)=a-Q, where a is a constant number and Q=q1+q2.nAll the above are common knowledgeJune 20, 2003973-347 Game Theory-Lecture 23Cournot duopoly model of incomplete information (version two) contdnFirm 2s marginal cost depends on some factor (e.g. technology) tha
11、t only firm 2 knows. Its marginal cost can be HIGH: cost function: C2(q2)=cHq2.LOW: cost function: C2(q2)=cLq2. nBefore production, firm 2 can observe the factor and know exactly its marginal cost is high or low. nHowever, firm 1 cannot know exactly firm 2s cost. Equivalently, it is uncertain about
12、firm 2s payoff. nFirm 1 believes that firm 2s cost function isC2(q2)=cHq2 with probability , andC2(q2)=cLq2 with probability 1.June 20, 20031073-347 Game Theory-Lecture 23Cournot duopoly model of incomplete information (version two) contdnFirm 1s marginal cost also depends on some other independent
13、factor that only firm 1 knows. Its marginal cost can be HIGH: cost function: C1(q1)=cHq1.LOW: cost function: C1(q1)=cLq1. nBefore production, firm 1 can observe the factor and know exactly its marginal cost is high or low. nHowever, firm 2 cannot know exactly firm 1s cost. Equivalently, it is uncert
14、ain about firm 1s payoff. nFirm 2 believes that firm 1s cost function isC1(q1)=cHq1 with probability , andC1(q1)=cLq1 with probability 1.June 20, 20031173-347 Game Theory-Lecture 23Cournot duopoly model of incomplete information (version two) contdJune 20, 20031273-347 Game Theory-Lecture 23Cournot
15、duopoly model of incomplete information (version two) contdJune 20, 20031373-347 Game Theory-Lecture 23Cournot duopoly model of incomplete information (version two) contdJune 20, 20031473-347 Game Theory-Lecture 23Cournot duopoly model of incomplete information (version two) contdJune 20, 20031573-3
16、47 Game Theory-Lecture 23Cournot duopoly model of incomplete information (version two) contdJune 20, 20031673-347 Game Theory-Lecture 23Cournot duopoly model of incomplete information (version two) contdJune 20, 20031773-347 Game Theory-Lecture 23Cournot duopoly model of incomplete information (version two) contdJune 20, 20031873-347 Game Theory-Lecture 23Cournot duopoly model of
