Entry Deterrence with Public Signals: Revisiting the Chain-Store Paradox

We revisit the classic chain-store paradox by introducing exogenous public signals about the incumbent’s private type that arrive each period over a finite horizon. We fully characterize perfect Bayesian equilibria in terms of sequences of reputation cutoffs that increase over time: entrants enter below their cutoff, while the normal incumbent mixes below its cutoff and fights above it. The equilibrium outcome is generically unique. Information arrival dampens the incentive to build a reputation, so full deterrence need not emerge as the horizon grows arbitrarily long, even when the incumbent is very patient. We characterize exactly when there is full deterrence in the limit, along with the limiting equilibrium when there is not.