Consider the following payoff matrix for a game in which two firms attempt to collude under the Bertrand model:Firm B cuts Firm B colludesFirm A cuts 6,6 24,0Firm A colludes 0,24 12,12Here, 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.

In an oligopoly model proposed by Bertrand, enterprises individually decide on pricing (rather than quantity) in an effort to maximize profits. This is performed by taking the prices of competitors as given.

The resulting equilibrium, also known as a Bertrand (Nash) equilibrium, is a Nash equilibrium in prices.
The Bertrand competition model of competition pits two or more businesses against one another on pricing for a uniform good.
Theoretically, this price competition leads to the enterprises selling their products at marginal costs and making no profit since the commodities are perfect substitutes.

For the stated conditions,

The choices include colluding to keep the price at the collusive level or lowering the price to try to enhance the firm's market share (cut).

The payoffs are expressed as annual revenues in the millions of dollars.

Thus, then both firms cutting prices will be the game's Nash equilibrium.

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