In the game presented below the strategies are quantities of output the firm cou

Question

In the game presented below the strategies are quantities of output the firm could produce and the first payoff goes to firm 1 and the second to firm 2. This game is the correct game to use for parts (a) – (c).

a) Explain why producing 31 is a dominant strategy for firm 1.

b) Explain why this game is a prisoner’s dilemma.

c) Explain why this game could represent the behavior of two firms trying to collude and act like a monopoly.

d) Explain why the game below does not have a dominant strategy for either player.

e) Find the maximum equilibrium and a Nash equilibrium for the game below.

Explanation / Answer

a) 31 is a Dominant strategy for Firm 1 because no matter which choice Firm 2 makes, Firm 1 is better off having made choice 31 (1107 vs 1050 and 1045.5 vs 990). The same also happens to be true of Firm 2 (1107 vs 1050 and 1045.5 vs 990). b) It is a Prisoner's Dilemma because the optimal choice is for both firms to take choice 30 for a total of 2100 payout (30:31 or 31:30 yields 2097 and 31:31, the dominant strategy, yields 2091) c) If both firms were to signal or communicate, they could agree to both choose choice 30, so they are both better off, but the consumers are worse off. d) There is no dominant strategy for either firm, because the payout on either choice can be worse or better than the other choice depending on the other firm's decision. e) The maximum equilibrium is at 25:30 (A=600,B=600). Nash equilibrium is at 16:30 (A=800,B=1000).

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