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
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 2
Today's Agenda What is a static game of incomplete information? Prisoners'dilemma of incomplete information Cournot duopoly model of incomplete information Battle of sexes of incomplete information First-price auction 3
Today’s Agenda ◼ What is a static game of incomplete information? ◼ Prisoners’ dilemma of incomplete information ◼ Cournot duopoly model of incomplete information ◼ Battle of sexes of incomplete information ◼ First-price auction 3
Static (or simultaneous-move)games of complete information A set of players (at least two players) For each player,a set of strategies/actions Payoffs received by each player for the combinations of the strategies,or for each player,preferences over the combinations of the strategies All these are common knowledge among all the players
Static (or simultaneous-move) games of complete information ◼ A set of players (at least two players) ◼ For each player, a set of strategies/actions ◼ Payoffs received by each player for the combinations of the strategies, or for each player, preferences over the combinations of the strategies ◼ All these are common knowledge among all the players. 4
Static (or simultaneous-move)games of INCOMPLETE information Payoffs are no longer common knowledge Incomplete information means that >At least one player is uncertain about some other player's payoff function (type) Static games of incomplete information are also called static Bayesian games
Static (or simultaneous-move) games of INCOMPLETE information ◼ Payoffs are no longer common knowledge ◼ Incomplete information means that ➢ At least one player is uncertain about some other player’s payoff function (type) ◼ Static games of incomplete information are also called static Bayesian games 5
Prisoners'dilemma of complete information Two suspects held in separate cells are charged with a major crime. However,there is not enough evidence. ■ Both suspects are told the following policy: >If neither confesses then both will be convicted of a minor offense and sentenced to one month in jail. >If both confess then both will be sentenced to jail for six months. If one confesses but the other does not,then the confessor will be released but the other will be sentenced to jail for nine months. Prisoner 2 Mum Confess Mum -1 -1 -9 Q Prisoner 1 Confess 0 -9 -6,-6 6
Prisoners’ dilemma of complete information Prisoner 2 Mum Confess Prisoner 1 Mum -1 , -1 -9 , 0 Confess 0 , -9 -6 , -6 6 ◼ Two suspects held in separate cells are charged with a major crime. However, there is not enough evidence. ◼ Both suspects are told the following policy: ➢ If neither confesses then both will be convicted of a minor offense and sentenced to one month in jail. ➢ If both confess then both will be sentenced to jail for six months. ➢ If one confesses but the other does not, then the confessor will be released but the other will be sentenced to jail for nine months