Price competition when three are few and four are many

I examine price competition in a market for a homogeneous good when consumers observe prices subject to a random shock (perception error). When firms have symmetric costs, there exists a unique equilibrium in pure strategies, which is symmetric. When there are up to three sellers in the market, the sellers extract the entire consumer surplus. However, with at least four firms, assuming that the marginal cost is sufficiently low relative to consumers' valuation, both consumers and producers may enjoy a positive surplus. The marginal-cost pricing is never observed in an equilibrium with finitely many firms. Potential policy implications are discussed.