國外博弈論課件lecture(24)-資料下載頁
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【正文】 tions: u1(q1, q2)=q1(a(q1+q2)c), u2(q1, q2)=q2(a(q1+q2)c) May 19, 2021 73347 Game TheoryLecture 1 19 One More Example ? Each of n players selects a number between 0 and 100 simultaneously. Let xi denote the number selected by player i. ? Let y denote the average of these numbers ? Player i’s payoff = xi – 3y/5 ? The normalform representation: May 19, 2021 73347 Game TheoryLecture 1 20 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 1 , 1 9 , 0 0 , 9 6 , 6 Prisoner 1 Prisoner 2 Confess Mum Confess Mum Players Strategies Payoffs May 19, 2021 73347 Game TheoryLecture 1 21 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 1 , 1 9 , 0 0 , 9 6 , 6 Prisoner 1 Prisoner 2 Confess Mum Confess Mum regardless of other players’ choices si” is strictly better than si’ May 19, 2021 73347 Game TheoryLecture 1 22 Summary ? Static (or simultaneousmove) games of plete information ? Normalform or strategicform representation ? Next time ? Dominated strategies ? Iterated elimination of strictly dominated strategies ? Nash equilibrium ? Reading lists ? Sec of Gibbons and Sec , and of Osborne
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