Collusion and multimarket contact in a repeated game

The ability of oligopolistic firms tacitly to exploit their potential market power and achieve better outcomes than the non-cooperative Nash equilibrium was first analyzed by Friedman (1971). Friedman argued that in an infinitely repeated game, the threat of future punishment can be used to enforce cooperative behavior. Starting from a collusive output level, duopolists may define future reactions to deviation from that output level (trigger or grim strategies), by which both the deviating and the punishing firm are hurt. Following Friedman, the sustainability of the collusive equilibrium can then be measured by calculating the critical discount factor that equalizes the long term gains from a collusive strategy with the gains from a deviating strategy. In a seminal article, Bernheim / Whinston (1990) claim that multimarket contact may help firms to sustain collusive outcomes whenever firms or markets differ from each other. They consider firms that compete in several markets. It is shown, that the opportunity these firms have to punish deviation from a cooperative equilibrium in every “contact” market may relax binding incentive constraints in a wide range of circumstances. Furthermore, whenever firms differ in their production costs or when scale economies are present, multimarket contact allows the development of “spheres of influence”, which enables firms to sustain higher levels of profits and prices. Bernheim and Whinston assume that markets are independent of one another. The mechanism driving their result is that the ability for multimarket firms to “pool” their incentive constraints across markets allows them to export “slack enforcement power” from one market to the other.