Dynamic Limit Pricing

This paper studies a simple multi-period model of limit pricing under one-sided incomplete information. I characterize pooling and separating equilibria, determine conditions under which the latter exist and study under which conditions on the primitives the equilibria involve limit pricing. The results are compared to a static benchmark. I identify two regimes that depend on the primitives of the model, namely a monopoly price regime and a limit price regime. In the former, the unique reasonable equilibrium involves immediate separation on monopoly prices. In the latter, I identify a unique class of reasonable limit price equilibria in which different types may initially pool for an arbitrary amount of time and then (possibly) separate. I argue that in a reasonable equilibrium, all signaling takes place in a single period (if the informed player is able to do so). If separation occurs in finite time, this involves setting prices that are so low that the inefficient incumbent's profits from mimicking are strictly negative. With a sufficiently high discount factor, the losses from mimicking may become arbitrarily large.