Consider the following payoff matrix for a game in which two firms attempt to collude under the Bertrand model:

Here, the possible options are to retain the collusive price (collude) or to lower the price in attempt to increase the firm's market share (cut). The payoffs are stated in terms of millions of dollars of profits earned per year. What is the Nash equilibrium for this game?

Question

Consider the following payoff matrix for a game in which two firms attempt to collude under the Bertrand model:

Here, the possible options are to retain the collusive price (collude) or to lower the price in attempt to increase the firm's market share (cut). The payoffs are stated in terms of millions of dollars of profits earned per year. What is the Nash equilibrium for this game?

Quizplus · Accepted Answer

In this game, both firms have a dominant strategy to cut prices because if one firm colludes and the other cuts, the cutting firm earns a higher profit. However, if both firms cut prices, they earn less than if they were to collude. Therefore, there are two Nash equilibria: A cuts and B colludes, and A colludes and B cuts. In both cases, neither player can benefit from unilaterally deviating from their strategy, given the other player's strategy.

Consider the Following Payoff Matrix for a Game in Which