Gryglewicz, S. and Kolb, A. (2023). Strategic Pricing in Volatile Markets Operations Research, :.

We study dynamic entry deterrence through limit pricing in markets subject to persistent demand shocks. An incumbent is privately informed about its costs, high or low, and can deter a Bayesian potential entrant by setting its prices strategically. The entrant can irreversibly enter the market at any time for a fixed cost, earning a payoff that depends on the market conditions and the incumbent{\textquoteright}s unobserved type. Market demand evolves as a geometric Brownian motion. When market demand is low, entry becomes a distant threat, so there is little benefit to further deterrence, and, in equilibrium, a weak incumbent becomes tempted to reveal itself by raising its prices. We characterize a unique equilibrium in which the entrant enters when market demand is sufficiently high (relative to the incumbent{\textquoteright}s current reputation), and the weak incumbent mixes over revealing itself when market demand is sufficiently low. In this equilibrium, pricing and entry decisions exhibit path dependence, depending not only on the market{\textquoteright}s current size, but also its historical minimum.