ABSTRACT We study the feasibility and profitability of predation in a dynamic environment, using a parsimonious infinite‐horizon, complete information setting in which an incumbent repeatedly faces potential entry. When a rival enters, the incumbent chooses whether to accommodate or predate it; the entrant then decides whether to stay or exit. We show that there always exists a Markov perfect equilibrium, which can be of three types: accommodation, monopolization, and recurrent predation. We then analyze and compare the welfare effects of different antitrust policies, accounting for the possibility that recurrent predation may be welfare improving.