Consider the following payoff matrix for a game in which two firms attempt to collude under the Bertrand model: Firm B cuts Firm B colludes
Firm A cuts 6,6 24,8
Firm A colludes 8,24 12,12

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. B cuts and A colludes.
d. A cuts and B colludes.

A

Explanation:

Game theory looks at the interactions between participants in a competitive game and calculates the best choice for the player.

Dominant strategy is the best option for a player regardless of what the other player is playing.

Nash equilibrium is the best outcome for players where no player has an incentive to change their decisions.

For either firm, the payoff of cutting price is either 6 or 24

For either firm, the payoff of colluding is either 8 or 12

the dominant strategy for both firms is to cut price because it is the best option regardless of what the other firm does as it yields the highest payoffs.

Thus, the Nash equilibrium is to cut price

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