Price Wars in Finite Sequential Move Price Competition

This Paper characterises the unique Markov equilibrium in the sequential move, finite horizon pricing duopoly with discounting. Simple, short cycles repeat until the last two periods. For discount factors above 0.75488, there are three-period reaction function cycles and below 0.75488, two-period cycles. The equilibrium path in the latter case has continued E-undercutting at high prices, followed by infrequent but regular price wars. In a price war, a firm lowers all the way to a trigger level low enough to induce rivals to raise prices in the next period. While the price war is costly, both firms benefit in form of a higher market price in the following periods. Average long-run industry profits are bounded below by half the monopoly level, and are non-monotonic in the discount factor.