Question

Two firms are competing in an oligopolistic industry. Firm 1, the larger of the two firms are contemplating its capacity strategy, which could be either “aggressive” or “ passive”. Firm 2, the smaller competitor, is also pondering its capacity expansion strategy and a passive strategy. The following table shows the profits associated with each pair of choices:

Firm 1	Firm 2
	Aggressive	Passive
Aggressive	25, 9	33, 10
Passive	30, 13	36, 12

a. If both decide their strategies simultaneously, what is the Nash equilibrium?

b. If firm 1 could move first and credibly commit to its capacity expansion strategy, what is its optimal strategy? Draw the gram tree and show the equilibrium strategy.

Answer 1

Answer;

1. (Passive, Aggressive) with payoff (30, 13) is the Nash equilibrium if they move simultaneously.

reason; When Firm 2 chooses Aggressive, Firm 1 should choose Passive (Because payoff of 30 is greater than 25). If Firm 2 chooses Passive, Firm 1 should choose Passive (36>33). Similarly if Firm 1 chooses Aggressive, Firm 2 should choose Passive (10>9). If Firm 1 chooses Passive, Firm 2 should choose Aggressive (13>9). Thus (Passive, Aggressive) coincides.

2. Firm moves first:

Firm 1's optimum strategy is to go Aggressive. That's because, he will decide his strategy by checking Firm 2's response first. If he moves Aggressive, Firm 2 will choose Passive (10>9). If he moves Passive, Firm 2 will choose Agressive (13>12). Between the two responses of Firm 2, Firm 1 will benefit with Firm 2's first response. (33>30).

So Firm 1's optimum strategy is to move Aggressive,a nd Firm 2 will follow with Passive.