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Exercise: Payoff matrix -Oligopoly market-

You are given a payoff matrix for two firms in an oligopoly market.

  • Find the dominant strategy (if any) for each firm.
  • What profit would they each earn if they form a cartel (if possible)?
  • Can the cartel hold in the long run? If not, what is the long run equilibrium?

Payoff Matrix: Firm A: high prices Firm A: low prices
Firm B: high pricesA: $1000
B: $1000		A: $1200
B: $800
Firm B: low pricesA: $600
B: $1200		A: $700
B: $700

The dominant strategy for firm A is to charge a low price for its product. You can see that no matter what firm B chooses, firm A is always better off by choosing the low price option (i.e its profit is always bigger than if it had charged a high price).

The strategy for firm B depends on the choices firm A makes. If firm A charges a high (low) price then firm B should charge a low (high) price.

In order to find the point at which the firms would collude (i.e act as one monopolistic firm), find the point(s) where the sum of economic profits is the greatest. Then choose the points that benefit both parties. In our case we see that the sum of the first entries in each column are equal to one another and greater than the rest of the sums in each entry in the matrix. As we will see, the long run equilibrium prevents the firms from colluding.
  • Since we know that the firm A will charge a low price, it makes sense for firm B to charge a high price in order to maximize its profit. Then, we see that the long run equilibrium is in the upper right entry of the payoff matrix. Firm A has no incentive to form a cartel with firm B. 

Reference: Exercise inspired by: Mayer,David. AP Microeconomics Crash Course. Research & Education Association (2014). p 123. 

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