國外博弈論課件lecture(10)(編輯修改稿)
2024-11-14 12:47 本頁面
【文章內(nèi)容簡介】 oner 1’s best response to prisoner 2’s choice (Confess if rational, Mum if altruistic). ? (Confess if rational, Mum if altruistic) is prisoner 2’s best response to prisoner 1’s Confess ? A Nash equilibrium called Bayesian Nash equilibrium June 19, 2021 73347 Game TheoryLecture 22 10 Cournot duopoly model of plete information ? The normalform representation: ? Set of players: { Firm 1, Firm 2} ? Sets of strategies: S1=[0, +∞), S2=[0, +∞) ? Payoff functions: u1(q1, q2)=q1(a(q1+q2)c), u2(q1, q2)=q2(a(q1+q2)c) ? All these information is mon knowledge June 19, 2021 73347 Game TheoryLecture 22 11 Cournot duopoly model of inplete information ? A homogeneous product is produced by only two firms: firm 1 and firm 2. The quantities are denoted by q1 and q2, respectively. ? They choose their quantities simultaneously. ? The market price: P(Q)=aQ, where a is a constant number and Q=q1+q2. ? Firm 1’s cost function: C1(q1)=cq1. ? All the above are mon knowledge June 19, 2021 73347 Game TheoryLecture 22 12 Cournot duopoly model of inplete information cont’d ? Firm 2’s marginal cost depends on some factor (. technology) that only firm 2 knows. Its marginal cost can be ? HIGH: cost function: C2(q2)=cHq2. ? LOW: cost function: C2(q2)=cLq2. ? Before production, firm 2 can observe the factor and know exactly which level of marginal cost is in. ? However, firm 1 cannot know exactly firm 2’s cost. Equivalently, it is uncertain about firm 2’s payoff. ? Firm 1 believes that firm 2’s cost function is ? C2(q2)=cHq2 with probability ?, and ? C2(q2)=cLq2 with probability 1–?. ? All the above are mon knowledge June 19, 2021 73347 Game TheoryLecture 22 13 Cournot duopoly model of inplete information cont’d A s
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