When a market contains only a few significant competitors, each firm's profit depends on what its rivals do, and the natural framework is game theory, the study of strategic decision-making in which each player's payoff depends on the actions of all. A central solution concept is the Nash equilibrium, a set of strategies in which no player can improve their payoff by unilaterally changing strategy. Some games have a dominant strategy, one that yields the highest payoff regardless of what the other players do, which simplifies equilibrium analysis. When no pure-strategy equilibrium exists, players may use a mixed strategy, randomizing over actions with specific probabilities to keep opponents indifferent.
The most famous illustration is the Prisoner's Dilemma, in which two players pursuing their own self-interest reach an outcome that is worse for both than mutual cooperation would have been. In oligopoly, the Prisoner's Dilemma explains why firms have an incentive to cheat on collusive agreements: individual profit maximization leads to a Nash equilibrium that delivers lower joint profits than cooperation. Cooperation can sometimes be sustained in a repeated game, where the same interaction occurs many times and players value future payoffs. Strategies like tit-for-tat, cooperating when the other cooperates and punishing defection, can support cooperative equilibria over the long horizon.
Strategic considerations also shape pricing. In a sequential game, players move in turn, and such games are analyzed using a game tree and solved by backward induction, starting from the final decision nodes and reasoning back to the beginning. A credible threat is one that the threatener would actually find it in their interest to carry out; non-credible threats are dismissed in equilibrium. Firms with market power may practice price discrimination to extract more surplus. First-degree (perfect) price discrimination charges each consumer their maximum willingness to pay, capturing all consumer surplus. Second-degree price discrimination uses quantity or product-version discounts, such as bulk pricing or tiered menus. Third-degree price discrimination charges different prices to identifiable groups with different elasticities, like student or senior discounts. For any price discrimination to be viable, the firm must have market power, must be able to identify groups with different elasticities, and must prevent resale or arbitrage between groups.