Question

3) Use the information in the following table, which summarizes the payoffs (i.e., profit) to two firms that must decide between an average-quality and a high quality product, to answer the questions that follow: Firm 2 Average Quality High Quality Firm 1 Average Quality 600, 600 400, 1100 High Quality 1100, 400 900, 900 a. What is each player's dominant strategy? Explain your reasoning. b. Referring to the table above, is this an example of a prisoner's dilemma game? Why or why not? c. Is there a Nash equilibrium? If so, what is it?

Answer 1

Q3) Finding the dominant startegy by using the best responses:

Firm 1:

If firm 2 chooses average quality, the BR for firm 1 is to choose high quality (1100>600)

If firm 2 chooses high quality, the BR for firm 1 is to choose high quality (900>400)

Since, choosing high quality is the best response irrespective the choice of firm 2, this is the dominant vstrategy for firm 1.

Firm 2:

If firm 1 chooses average quality, the BR for firm 2 is to choose high quality (1100>600)

If firm 1 chooses high quality, the BR for firm 2 is to choose high quality (900>400)

Since, choosing high quality is the best response irrespective the choice of firm 1, this is the dominant vstrategy for firm 2.

(b) No this is not the form of a prisonners dillema game as the dominantv startegy is nsuch that both the palyers are coordinating on the best stratgey for them (maximum collective payoff). It would have been a prisoner's dilemma if the dominant strategy for both the players would have been to produce the average quality.

(c) From the best responses, it is observed that there is a unique Nash equilibrium where both Firm 1 and Firm 2 chooses the high-quality product.