國(guó)外博弈論課件lecture(18)(編輯修改稿)
2024-11-14 12:47 本頁(yè)面
【文章內(nèi)容簡(jiǎn)介】 player 2 plays F if player 1 plays C, plays H if player 1 plays D, plays K if player 1 plays E. Player 1 C D Player 2 F G 1, 0 0, 1 Player 2 J K 1, 3 2, 2 Player 2 H I 2, 1 1, 1 E June 10, 2021 73347 Game TheoryLecture 15 13 Multiple subgameperfect Nash equilibria ? Subgameperfect Nash equilibrium (D, FIK). ? player 1 plays D。 ? player 2 plays F if player 1 plays C, plays I if player 1 plays D, plays K if player 1 plays E. Player 1 C D Player 2 F G 1, 0 0, 1 Player 2 J K 1, 3 2, 2 Player 2 H I 2, 1 1, 1 E June 10, 2021 73347 Game TheoryLecture 15 14 Stackelberg model of duopoly ? A homogeneous product is produced by only two firms: firm 1 and firm 2. The quantities are denoted by q1 and q2, respectively. ? The timing of this game is as follows: ? Firm 1 chooses a quantity q1 ?0. ? Firm 2 observes q1 and then chooses a quantity q2 ?0. ? The market priced is P(Q)=a –Q, where a is a constant number and Q=q1+q2. ? The cost to firm i of producing quantity qi is Ci(qi)=cqi. ? Payoff functions: u1(q1, q2)=q1(a–(q1+q2)–c) u2(q1, q2)=q2(a–(q1+q2)–c) June 10, 2021 73347 Game TheoryLecture 15 15 Stackelberg model of duopoly ? Find the subgameperfect Nash equilibrium by backward induction ? We first solve firm 2’s problem for any q1 ?0 to get firm 2’s best response to q1 . That is, we first solve all the subgames beginning at firm 2. ? Then we solve firm 1’s problem. That is, solve the subgame beginning at firm 1 June 10, 2021 73347 Game TheoryLecture 15 16 Stackelberg model of duopoly ? Solve firm 2’s problem for any q1 ?0 to get firm 2’s best response to q1. ? Max u2(q1, q2)=q2(a–(q1+q2)–c) subject to 0 ? q2 ? +∞ FOC: a – 2q2 – q1 – c = 0 ? Firm 2’s best response, ? R2(q1) = (a – q1 – c)/2 if q1 ? a– c = 0 if q1 a– c Note: Osborne used b2(q1) instead of R2(q1) June 10, 2021 73347 Game TheoryLecture 15 17 Stackelberg model
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