国外博弈论课件lecture2.pptVIP

May 20, 2003 73-347 Game Theory--Lecture 2 May 20, 2003 Lecture 2 Static (or Simultaneous-Move) Games of Complete Information Dominated Strategies Nash Equilibrium Outline of Static Games of Complete Information Introduction to games Normal-form (or strategic-form) representation Iterated elimination of strictly dominated strategies Nash equilibrium Review of concave functions, optimization Applications of Nash equilibrium Mixed strategy equilibrium Today’s Agenda Review of previous class Dominated strategies Iterated elimination of strictly dominated strategies Nash equilibrium Review The normal-form (or strategic-form) representation of a game G specifies: A finite set of players {1, 2, ..., n}, players’ strategy spaces S1 S2 ... Sn and their payoff functions u1 u2 ... un where ui : S1 × S2 × ...× Sn→R. Review Static (or simultaneous-move) game of complete information Each player’s strategies and payoff function are common knowledge among all the players. Each player i chooses his/her strategy si without knowledge of others’ choices. Then each player i receives his/her payoff ui(s1, s2, ..., sn). The game ends. Solving Prisoners’ Dilemma Confess always does better whatever the other player chooses Dominated strategy There exists another strategy which always does better regardless of other players’ choices Definition: strictly dominated strategy Example Two firms, Reynolds and Philip, share some market Each firm earns $60 million from its customers if neither do advertising Advertising costs a firm $20 million Advertising captures $30 million from competitor 2-player game with finite strategies S1={s11, s12, s13} S2={s21, s22} s11 is strictly dominated by s12 if u1(s11,s21)u1(s12,s21) and u1(s11,s22)u1(s12,s22). s21 is strictly dominated by s22 if u2(s1i,s21) u2(s1i,s22), for i = 1, 2, 3 Definition: weakly dominated strategy Strictly and weakly dominated strategy A rational player never chooses a strictly dominated strategy. Hence, any strictly d