国外博弈论课件lecture25.ppt

June 24, 2003 73-347 Game Theory--Lecture 25 June 24, 2003 Lecture 25 Static (or Simultaneous-Move) Games of Incomplete Information Bayesian Nash Equilibrium Outline of Static Games of Incomplete Information Introduction to static games of incomplete information Normal-form (or strategic-form) representation of static Bayesian games Bayesian Nash equilibrium Auction Today’s Agenda Review of previous class Battle of sexes with incomplete information (version two) First-price sealed-bid auction Static Bayesian games Bayesian Nash equilibrium: 2-player Bayesian Nash equilibrium: 2-player 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: Both would like to spend the evening together. But Chris prefers the opera. Pat prefers the prize fight. Battle of the sexes with incomplete information (version two) Pat’s preference depends on whether he is happy. If he is happy then his preference is the 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 preference 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. Battle of the sexes with incomplete information (version two) cont’d Check whether ((Opera if happy, Opera if unhappy), (Opera if happy, Fight is unhappy)) is a Bayesian NE Battle of the sexes with incomplete information (version two) cont’d Battle of the sexes with incomplete information (version two) cont’d Battle of the sexes with incomplete information (version two) cont’d Battle of the sexes with incomplete information (version two)