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 regardless of what the other firm does. However, if both firms cut prices, they end up with a lower profit than if they both collude. Therefore, there is a temptation to collude. But if one firm chooses to collude while the other cuts prices, that firm will earn a much higher profit (10 vs 2). Therefore, there are two Nash equilibria: either both firms cut prices (as they would do with a dominant strategy), or one firm colludes while the other cuts prices (as neither firm has a dominant strategy in this case).

Consider the Following Payoff Matrix for a Game in Which