Oligopoly, Payoff Matrices and Nash Equilibrium

Interdependence is the defining feature

An oligopoly is a market with a few large firms and significant barriers to entry. What makes it different from every other structure is mutual interdependence: the best price for one firm depends on what the rivals do, so the firm cannot simply read an answer off its own cost curves.

Reading a payoff matrix

Each cell lists the payoff to the row player first and the column player second. Two tools do almost all the work:

• A dominant strategy gives a player a higher payoff no matter what the rival chooses. Test it by comparing that player's own numbers down a column (for the row player) or across a row (for the column player).
• A Nash equilibrium is an outcome where neither player can gain by changing strategy alone, given what the other is doing. If both players have a dominant strategy, the cell where the two meet is the Nash equilibrium.

The prisoner's dilemma and cartels

A cartel agrees to restrict output and hold price up. The agreement is unstable because at the cartel price each member's marginal revenue exceeds its marginal cost, so cheating by selling a little more raises that member's profit. Since every member reasons the same way, low prices are the dominant strategy and the Nash equilibrium is worse for both firms than the cooperative outcome. Collusion becomes easier to sustain when the game is repeated, when there are few firms, and when cheating is easy to detect.