QUESTIONS 1Consider the following pay-off matrixes for the interaction of two fi

Question

QUESTIONS 1Consider the following pay-off matrixes for the interaction of two firms, A and X. They each have an aggressive or a passive strategy that they could adopt. The first pay-off in each pair is for A and the second is for X. In each case attempt to identify: a) the dominant strategy for each player b) the Nash equilibrium c) the cooperative equilibrium. Firm X choice Aggressive Passive 100, 100150, 50 50, 150175, 175 Firm A choice Aggressive 1 Passive Firm X choice Aggressive 100, 75 50, 60 Passive 160, 60 110, 80 Firm A choice Aggressive Passive i) Firm X choice AggressivePassive Firm A choice Aggressive 250, 110 320, 120 300, 240 Passive 130, 160

Explanation / Answer

1) a) There is no dominant strategy for either player.

b) There are 2 Nash equilibria given by (Aggressive, Aggressive) and (Passive,Passive).

c) The cooperative equilibrium is (Passive,Passive) which is the Pareto optimal outcome.

2) a) Aggressive is a dominant strategy for Firm A. There is no dominant strategy for Firm X.

b) There is one Nash equilibrium given by (Aggressive,Aggressive).

c) The cooperative outcome is (Passive,Passive) which is Pareto optimal.

3) a) Aggressive is the dominant strategy for Firm A. Passive is the dominant strategy for Firm X.

b) There is one Nash equilibrium given by (Aggressive,Passive).

c) (Aggressive,Passive) is also the cooperative outcome.

2. The outcome will remain the same even if the game is repeated provided the threat is credible.

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