Two firms sequentially choose quantities q1, q2 to produce an identical good. First, firm 1 chooses...
Two firms sequentially choose quantities q1, q2 to produce an identical good. First, firm 1 chooses q1, then firm 2 chooses q2. The price per unit in the market is p(q1, q2) = 1 − (q1 + q2). Assume that both firms have a constant marginal cost of zero. Both firms seek to maximize their profit.
a. Formulate this story as an extensive form game
b. Find all Nash equilibria of this game.
c. Find the Subgame Perfect Nash equilibria of this game
Homework Answers
A) monopoly output =0.5
Competitive output=1
Cournot output=0.33
Each firm have three strategy available monopoly, competitive and cournot output.
B)
Nash equilibrium is both firm choosing cournot output to produce.
3)subgame of firm 2 choosing when firm 1 chooses monopoly: firm 2 chooses cournot
Subgame of firm 2 choosing when firm 1 choose competitive: firm 2 chooses cournot .
Subgame of firm 2 choosing when firm 1 choose cournot: firm 2 choose cournot
Subgame of firm 1 choosing among three strategy : firm 1 choose cournot as it gives 0.11 compare to competitive which gives -0.33 and monopoly which gives 0.08.
So subgame perfect nash EQUILIBRIUM is both firm choosing cournot output to produce.
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