國外博弈論課件lecture(4)-資料下載頁
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【正文】 o a public good ? How to find a Nash equilibrium ? Solve person 1’s maximization problem Max u1(c1, c2*) = v1(c1 + c2*) + w1 – c1 subject to 0 ? c1 ? w1 11112112110 s o m ef o r ,1)( :A s s u m e1*)( 01*)( :FO Cwrrvccvccv???????????May 23, 2021 73347 Game TheoryLecture 5 19 Contributing to a public good ? How to find a Nash equilibrium ? Solve person 2’s maximization problem Max u2(c1*, c2) = v2(c1* + c2) + w2 – c2 subject to 0 ? c2 ? w2 22222122120 s o m ef o r ,1)( :A s s u m e1)*( 01)*( :FO Cwrrvccvccv???????????May 23, 2021 73347 Game TheoryLecture 5 20 Contributing to a public good ? How to find a Nash equilibrium ? The contribution pair (c1*, c2*) is a Nash equilibrium if 222211112122110 s o m ef o r ,1)( 0 s o m ef o r ,1)( :As s u m e1*)*( 1*)*( wrrvwrrvccvccv??????????????May 23, 2021 73347 Game TheoryLecture 5 21 Contributing to a public good ? Best response function ? Person 1’s best function to person 2’s contribution c2: R1(c2) = r1 – c2 if c2 r1。 =0, if c2 ? r1 ? Person 2’s best function to person 1’s contribution c1: R2(c1) = r2 – c1 if c1 r2 。 =0, if c1 ? r2 c1 c2 r2 r1 r2 r1 (r1, 0) is a NE Suppose that r1 r2 May 23, 2021 73347 Game TheoryLecture 5 22 Summary ? Bertrand model of duopoly ? Contributing to a public good ? Next time ? Mixed strategy Nash equilibrium ? Reading lists ? Chapter of Gibbons
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