Sequential Moves and Tacit Collusion: Reaction-Function Cycles in a Finite Pricing Duopoly

This paper analyzes a finite horizon, sequential move pricing duopoly, restricting attention to Markov-strategies. The solution yields stationary patterns, independent of initial conditions, where the reaction-functions follow cycles of three periods. The market price never settles down, and is at all times strictly above marginal cost. Long-run average industry profits are approximately 5/6 of the monopoly level. These results demonstrate that neither a long horizon, nor non-Markovian strategies are required for persistent profits in dynamic price-competition games.