From the following payoff matrix, where the payoffs are the profits or losses of the two...

From the following payoff matrix, where the payoffs are the profits or losses of the two firms, determine (a) whether Firm A has a dominant strategy, (b) whether Firm B has a dominant strategy, and (c) the optimal strategy for each firm. Explain. Firm B Low price High price Firm A Low price (1, 1) (3, -2) High price (-2, 3) (2, 2) Prisoner’s Dilemma

Expert Solution

Solution-

A. whether Firm A has a dominant strategy

No, doesn't have a dominant strategy. When firm B charges a low price, firm A will earn a profit of 1 when it also charges a low price and a profit of ?1 (i.e., a loss of 1) when it charges a high price. When firm B charges a high price, firm A earns a profit of 3 when it charges a low price and a profit of 4 when it charges a high price. Therefore, firm A does not have a dominant strategy.

B. Whether Firm B has a dominant strategy

Has a dominant strategy of low price When firm A charges a low price, firm B earns a profit of 1 when it also charges a low price and a profit of ?1 when it charges a high price. Similarly, when firm A charges a high price, firm B earns a profit of 3 when it charges a low price and a profit of 2 when it charges a high price. Therefore, charging a low price is the dominant strategy for firm B.

C. The optimal strategy for each firm.

The optimal strategy for firm B is its dominant strategy of charging a low price. The optimal strategy for firm A is a low price, given that firm B will charge a low price.

Prisoner’s Dilemma

The firm's face prisoner's dilemna because the option that creates the best profit payoff is for both firms to choose a high price strategy. However, neither firm can trust the other firm to charge a high price, so they choose their best or dominant strategy instead. Each firm could do better (earn higher profitts) if they both choose high price.

Rahul Sunny answered 2 years ago

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