國外博弈論課件lecture(4)(參考版)
2024-10-21 12:47本頁面
【正文】 =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 。 =0, ow. ? The cost to firm i of producing quantity qi is Ci(qi)=cqi. May 23, 2021 73347 Game TheoryLecture 5 11 Bertrand model of duopoly (homogeneous products) The normalform representation: ? Set of players: { Firm 1, Firm 2} ? Sets of strategies: S1=[0, +∞), S2=[0, +∞) ? Payoff functions: ??????????????????????????12212212222122121112111211 if0 if2/))(( if))(() ,( if0 if2/))(( if))(() ,(pppppacppppacpppupppppacppppacpppuMay 23, 2021 73347 Game TheoryLecture 5 12 Bertrand model of duopoly (homogeneous products) Best response functions: pm =( a + c )/2 ????????????????????????????????111122112212222211221121 if if if} :{ if} :{)( if if if} :{ if} :{)(pppppccppppcpppppBpppppccppppcpppppBmmmmmmMay 23, 2021 73347 Game TheoryLecture 5 13 Bertrand model of duopoly (homogeneous products) Best response functions: p1 p2 c c pm pm p1 p2 c c pm pm Firm 1’s best response to Firm 2’s p2 Firm 2’s best response to Firm 1’s p1 May 23, 2021 73347 Game TheoryLecture 5 14 Bertrand model of duopoly (homogeneous products)
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