第六讲 完美信息动态博弈：案例分析.pptVIP

第六讲 Extensive games with perfect information: illustrations 一、Stackelberg’s model of duopoly:constant unit cost and linear inverse demand Players：the two firms (a leader and a follower)； Timing：(1)firm 1 chooses a quantity ；(2) firm 2 observes and then chooses a quantity ; Preferences：Each firm’s preferences are represented by its profit. 基本假定 Constant unit cost： Linear inverse demand function： Assume： Backward induction First compute firm 2’s reaction to an arbitrary quantity by firm 1: Next firm 1’s problem in the first stage of the game amounts to: Thus the outcome of the game is: Conclusion The outcome of the equilibrium output is: Firm 1’s profit is , and firm 2’s profit is . By contrast, in the unique Nash equilibrium of Cournot’s (simultaneous-move) game under the same assumptions, each firm produces units of output and obtains the profit .Thus firm 1 produces more output and obtains more profit in the subgame perfect equilibrium of the sequential game, and firm 2 produces less output and obtains less profit. 二、Wages and employment in a unionized firm Players: a firm and a monopoly union; Timing: the union makes a wage demand w; the firm observes (and accepts) w and then chooses employment L. Preferences: the payoff of the union is and the payoff of the firm is . Backward induction First, we can characterize the firm’s best response in stage 2, to an arbitrary wage demanded by the union in stage 1, . The union’s problem at the first stage amounts to: Conclusion Thus (w*,L*(w*)) is the backwards-induction outcome of this wage-and-employment game. It is straightforward to see that (w*,L*(w*)) is inefficient. 三、Bargaining The ultimatum game (最后通谍博弈) A finite horizon game with alternating offers and impatient players An infinite horizon game with alternating offers and impatient players 三（1） The ultimatum game (最后通谍博弈) Players：the two