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1、June 24, 2003,73-347 Game Theory-Lecture 25,1,Static (or Simultaneous-Move) Games of Incomplete Information,Bayesian Nash Equilibrium,June 24, 2003,73-347 Game Theory-Lecture 25,2,Outline of Static Games of Incomplete Information,Introduction to static games of incomplete information Normal-form (or
2、 strategic-form) representation of static Bayesian games Bayesian Nash equilibrium Auction,June 24, 2003,73-347 Game Theory-Lecture 25,3,Todays Agenda,Review of previous class Battle of sexes with incomplete information (version two) First-price sealed-bid auction,June 24, 2003,73-347 Game Theory-Le
3、cture 25,4,Static Bayesian games,June 24, 2003,73-347 Game Theory-Lecture 25,5,Bayesian Nash equilibrium: 2-player,June 24, 2003,73-347 Game Theory-Lecture 25,6,Bayesian Nash equilibrium: 2-player,player 1s best response if her type is t1i,player 2s best response if her type is t2j,In the sense of e
4、xpectation based on her belief,In the sense of expectation based on her belief,June 24, 2003,73-347 Game Theory-Lecture 25,7,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: Bot
5、h would like to spend the evening together. But Chris prefers the opera. Pat prefers the prize fight.,June 24, 2003,73-347 Game Theory-Lecture 25,8,Battle of the sexes with incomplete information (version two),Pats preference depends on whether he is happy. If he is happy then his preference is the
6、same. If he is unhappy then he prefers to spend the evening by himself. Chris cannot figure out whether Pat is happy or not. But Chris believes that Pat is happy with probability 0.5 and unhappy with probability 0.5 Chris preference also depends on whether she is happy. If she is happy then her pref
7、erence is the same. If she is unhappy then she prefers to spend the evening by herself. Pat cannot figure out whether Chris is happy or not. But Pat believes that Chris is happy with probability 2/3 and unhappy with probability 1/3.,June 24, 2003,73-347 Game Theory-Lecture 25,9,Battle of the sexes w
8、ith incomplete information (version two) contd,Check whether (Opera if happy, Opera if unhappy), (Opera if happy, Fight is unhappy) is a Bayesian NE,June 24, 2003,73-347 Game Theory-Lecture 25,10,Battle of the sexes with incomplete information (version two) contd,June 24, 2003,73-347 Game Theory-Lec
9、ture 25,11,Battle of the sexes with incomplete information (version two) contd,June 24, 2003,73-347 Game Theory-Lecture 25,12,Battle of the sexes with incomplete information (version two) contd,June 24, 2003,73-347 Game Theory-Lecture 25,13,Battle of the sexes with incomplete information (version tw
10、o) contd,June 24, 2003,73-347 Game Theory-Lecture 25,14,Battle of the sexes with incomplete information (version two) contd,Chris believes that Pat is happy with probability 0.5, unhappy 0.5,Chris expected payoff of playing Fight if Chris is happy and Pat plays (Opera if happy, Fight if unhappy),Jun
11、e 24, 2003,73-347 Game Theory-Lecture 25,15,Battle of the sexes with incomplete information (version two) contd,Pat believes that Chris is happy with probability 2/3, unhappy 1/3,Pats expected payoff of playing Opera if Pat is unhappy and Chris plays (Fight if happy, Fight if unhappy),June 24, 2003,
12、73-347 Game Theory-Lecture 25,16,Battle of the sexes with incomplete information (version two) contd,Check whether (Fight if happy, Opera if unhappy), (Fight if happy, Fight is unhappy) is a Bayesian Nash equilibrium.,June 24, 2003,73-347 Game Theory-Lecture 25,17,First-price sealed-bid auction (3.2
13、.B of Gibbons),June 24, 2003,73-347 Game Theory-Lecture 25,18,First-price sealed-bid auction (3.2.B of Gibbons) contd,June 24, 2003,73-347 Game Theory-Lecture 25,19,First-price sealed-bid auction (3.2.B of Gibbons) contd,June 24, 2003,73-347 Game Theory-Lecture 25,20,First-price sealed-bid auction (
14、3.2.B of Gibbons) contd,June 24, 2003,73-347 Game Theory-Lecture 25,21,First-price sealed-bid auction (3.2.B of Gibbons) contd,June 24, 2003,73-347 Game Theory-Lecture 25,22,Summary,Battle of sexes with incomplete information (version two) First-price sealed-bid auction Next time Reading lists Chapter 3.1 of Gibbons Chapter 3.2.B of Gibbons,
