Suppose there are two similar firms in a market that are strategically interdepe

Question

Suppose there are two similar firms in a market that are strategically interdependent. Firm A and Firm B. Firm A is a larger firm than firm B. Basically each needs to determine whether to “collude” or to “cheat” in an oligopolistic market. If Firm A colludes and Firm B colludes then Firm A earns 1,000 and Firm B earns 100. If Firm A colludes and Firm B cheats then Firm A earns 800 and Firm B earns 200. If Firm A cheats and Firm B colludes then Firm A earns 1,050 and Firm B earns 50. If both firms cheat, Firm A earns 500 and Firm B earns 20. Present the game in a “tabular” or matrix format. What outcome do you expect in this game? Fully explain. One way to proceed is to say what is Firm A’s best choice if Firm B colludes and what is Firm A’s best choice if Frim B cheats. I am not going to commit and say there is one true answer here, you may need to dig a little deeper.

Explanation / Answer

The game is played by two firms: Firm A and Firm B. The strategy set faced by each firm is {Collude, Cheat}. After assigning the payoffs, construct the payoff matrix akin to the one described below:

Firm B

Firm A

Collude

Cheat

Collude

(1000, 100)

(800, 200)

Cheat

(1050, 50)

(500, 20)

The game certainly has no dominant strategy for any firm. Note that when Firm A choses Collude, Firm B is better off in choosing Cheat since this gives Firm B a payoff of $200 while Collude gives a payoff of $100. When Firm A choses Cheat, Firm B is better off in choosing Collude and gain $50 which is greater than $20 when it Cheats.

In a similar manner, when Firm B choses Collude, Firm A is better off in choosing Cheat, earning $1050 which is greater than the payoff of $1000 when it Colludes. And when Firm B choses Cheat, Firm A is better off in choosing Collude. So there are two pure strategy Nash equilibria: (Collude, Cheat) and (Cheat, Collude)

Firm B

Firm A

Collude

Cheat

Collude

(1000, 100)

(800, 200)

Cheat

(1050, 50)

(500, 20)

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