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?

A) Both firms cut prices.
B) Both firms collude.
C) There are two Nash equilibria: A cuts and B colludes, and A colludes and B cuts.
D) There are no Nash equilibria in 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?

A) Both firms cut prices.
B) Both firms collude.
C) There are two Nash equilibria: A cuts and B colludes, and A colludes and B cuts.
D) There are no Nash equilibria in this game.

prajakta belsare · Accepted Answer

Final Answer : C, Explanation :  The Nash equilibrium occurs when neither player has an incentive to change their strategy, given the other player's strategy. In this game, if A colludes, then B maximizes profits by also colluding. If A cuts, then B maximizes profits by cutting as well. Therefore, both (A cuts and B colludes) and (A colludes and B cuts) are Nash equilibria.

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