Two competing firms are each planning to introduce a new product. Each will decide whether to produce Product A, Product B, or Product C. They will make their choices at the same time. The resulting payoffs are shown below.

	FIRM 2
A	B	C
FIRM 1	A	-10, -10	0, 10	10, 20
B	10, 0	-20, -20	-5, 15
C	20, 10	15, -5	-30, -30

a. Are there any Nash equilibria in pure strategies? If so, what are they?

b. If both firms use maximin strategies, what outcome will result?

c. If Firm 1 uses a maximin strategy and Firm 2 knows this, what will Firm 2 do?

You can determine the optimal strategy for each firm by individually assessing the strategy opted for by one firm, given the choice of the other firm.

• If Firm 1 chooses A, Firm 2 will choose C to maximize its payoff.

• If Firm 1 chooses B, Firm 2 will choose C to maximize its payoff.

• If Firm 1 chooses C, Firm 2 will choose A to maximize its payoff.

Thus, Firm 2 does not have a dominant strategy.

• Similarly, if Firm 2 chooses A, Firm 1 will choose C to maximize its payoff.

• If Firm 2 chooses B, Firm 1 will choose C to maximize its payoff.

• If Firm 2 chooses C, Firm 1 will choose A to maximize its payoff.

Here you see that even Firm 1 does not have a dominant strategy.

However, from the definition of Nash equilibrium, you can observe that there are two pure strategy Nash equilibria in this game found at (A,C) and (C,A) with payoffs (10, 20), and (20,10), respectively. Thus, the two firms choose strategies A and C alternatively to reach the Nash equilibria from which neither is incentivized to deviate.

When the firms use maximin strategies, they aim to minimize their losses and opt for the strategy where they incur the highest yield.

The least payoff corresponding to each strategy chosen by Firm 1 is as follows:

The least payoff corresponding to each strategy chosen by Firm 2 is as follows:

Thus, both firms will be able to minimize their losses by producing Product A. In such a case, the firms will attain equilibrium at (A, A) and receive the payoff (-10, -10).

The outcome of the maximin strategy is significantly lower than the outcomes attained by the pure strategy Nash equilibria.

Part (b) shows that Firm 1 will opt for A by using a maximin strategy. If Firm 2 is aware of this decision, it will decide to produce Product C and earn a payoff worth 20 units. Thus, the firms will attain equilibrium at point (A, C) and receive payoffs (10, 20), which corresponds to one of the Nash equilibria.

Thus, Firm 2 benefits in this situation as the firms operate at the Nash equilibrium where the payoff received by Firm 2 is higher than at the point (C, A).