consider a model with three symmetric firms competing in quantities and facing a linear demand p(Q)=a-Q,where Q is the aggregate supply.Firm 1 moves first and chooses its quantity.Firm 2 and 3 observe that chosen quantity and then simultaneously choose their quantities.Assume marginal cost of production is zero for each firm. what is the (subgame perfect) Nash equilibrium in quantities? what is the quilibrium price?
想象一个有3个公司竞争进行产量竞争的模型,他们面对线性需求p(Q)=a-Q,这里Q是累计供给量。公司1先行动,选择产量。公司2和公司3根据公司1选择的产量同时进行他们的产量选择。想象每个公司的边际成本是0。子博弈完美产量纳什平衡是什么?平衡价格是多少?
我做的答案是(a/6,a/3,a/3),价格是a/6,但觉得不对。。。
这里说公司2公司3 根据公司1的价格做决定,是不是要先列公司一的方程式,然后把公司1的最优产量带到公司2和3中。。。。