Summary: The degree of collusiveness of a market with consumer switching costs is analyzed in an infinite-horizon model of duopolistic competition. In contrast with previous analyses, we assume that firms compete for the demand for a homogeneous good by setting prices simultaneously in each period. This problem is formulated as a simple stochastic game, and a symmetric stationary Markovian perfect equilibrium with distinctive economic features is studied. We show that switching costs unambiguously relax price competition in equilibrium but that, on the contrary, they may make tacit collusion more difficult to sustain.