Abstract: This article analyzes entry–exit decisions in a market where reputation determines the price that firms may charge, within a rational-expectation model of competition in a nonatomic market under heterogeneous reputations. The analysis focuses on the class of name-switching reputational equilibria, in which a firm discards its name if and only if its reputation falls below the entrants’ reputation. The main technical result is the existence of a unique steady-state equilibrium within this class, in which the entrants’ reputation is endogenous. The resulting industry dynamics is largely on agreement with the findings in the empirical literature. © (2017) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association