國外博弈論課件lecture(24)(編輯修改稿)
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【文章內(nèi)容簡介】 rategy without knowledge of others’ choices. ? Complete information ? Each player’s strategies and payoff function are mon knowledge among all the players. ? Assumptions on the players ? Rationality ? Players aim to maximize their payoffs ? Players are perfect calculators ? Each player knows that other players are rational May 19, 2021 73347 Game TheoryLecture 1 11 Static (or simultaneousmove) games of plete information ? The players cooperate? ? No. Only noncooperative games ? The timing ? 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. May 19, 2021 73347 Game TheoryLecture 1 12 Definition: normalform or strategicform representation ?The normalform (or strategicform) 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 . May 19, 2021 73347 Game TheoryLecture 1 13 Normalform representation: 2player game ? Bimatrix representation ? 2 players: Player 1 and Player 2 ? Each player has a finite number of strategies ? Example: S1={s11, s12, s13} S2={s21, s22} Player 2 s21 s22 Player 1 s11 u1(s11,s21), u2(s11,s21) u1(s11,s22), u2(s11,s22) s12 u1(s12,s21), u2(s12,s21) u1(s12,s22), u2(s12,s22) s13 u1(s13,s21), u2(s13,s21) u1(s13,s22), u2(s13,s22) May 19, 2021 73347 Game TheoryLecture 1 14 Classic example: Prisoners’ Dilemma: normalform representation ? Set of players: {Prisoner 1, Prisoner 2} ? Sets of strategies: S1 = S2 = {Mum, Confess} ? Payoff functions: u1(M, M)=1, u1(M, C)=9, u1(C, M)=0, u1(C, C)=6。 u2(M, M)=1, u2(M, C)=0, u2(C, M)=9, u2(C, C)=6 1 , 1 9 , 0 0 , 9 6 , 6 Prisoner 1 Prisoner 2 Confess Mum Con
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