Firms Acme and Best operate in a market with demand given by: P(Q) = 100 - Q. Each firm has costs given by: C(Q) = 10Q. Each firm has three possible output levels: 25, 30, and 40. For parts (a) through (c), assume that the firms simultaneously choose their output level.
(a) Construct the 3 by 3 payoff matrix to illustrate the returns (in this case, the profits) from choosing the various output combinations.
(b) What is Acme's strategy? Is this a dominant strategy?
(c) What is the Nash equilibrium of this game?
(d) Now assume that the firms sequentially choose their output levels with Acme choosing first. Describe the game using a game tree.