國外博弈論課件lecture(6)(已修改)
2024-10-30 12:48 本頁面
【正文】 May 21, 2021 73347 Game TheoryLecture 3 1 Static (or SimultaneousMove) Games of Complete Information Nash Equilibrium Best Response Function May 21, 2021 73347 Game TheoryLecture 3 2 Outline of Static Games of Complete Information ? Introduction to games ? Normalform (or strategicform) representation ? Iterated elimination of strictly dominated strategies ? Nash equilibrium ? Review of concave functions, optimization ? Applications of Nash equilibrium ? Mixed strategy Nash equilibrium May 21, 2021 73347 Game TheoryLecture 3 3 Today’s Agenda ? Review of previous classes ? Nash equilibrium ? Best response function ? Use best response function to find Nash equilibria ? Examples May 21, 2021 73347 Game TheoryLecture 3 4 Review ? 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 . Prisoner 2 Mum Confess Prisoner 1 Mum 1 , 1 9 , 0 Confess 0 , 9 6 , 6 All binations of the strategies. A bination of the strategies is a set of strategies, one for each player May 21, 2021 73347 Game TheoryLecture 3 5 Review ? Static (or simultaneousmove) game of plete information ? Each player’s strategies and payoff function are mon 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. May 21, 2021 73347 Game TheoryLecture 3 6 In th e no rm al fo rm g a me { S1 , S2 , ..., Sn , u1 , u2 , ... , un}, let si39。 , si ? Si b e feas ib le strategies fo r p la y er i . Strateg y si39。 is strictly do mi na ted by strat egy si if ui( s1, s2, ... si 1, si39。 , si+ 1, . .., sn) ui( s1, s2, ... si 1, si , si+ 1, ... , sn) fo r all s1? S1, s2? S2, . . ., si 1? Si 1, si+ 1? Si + 1, ..., sn? Sn. Definition: strictly dominated strategy regardless of other players’ choices si” is strictly better than si’ Prisoner 2 Mum Confess Prisoner
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