Abstract We study a model of price competition in a homogeneous good market where consumers may be fully rational or inattentive to small price differences. At the beginning, firms are pricing at marginal cost, and receive a stochastic signal concerning consumers’ rationality. They then compete for two periods, observing the market outcome at the end of the first. We characterize an equilibrium in which, when consumers are effectively inattentive (and at least one firm receives the correct signal), the market price converges to the monopoly level by the second period. This is achieved after a first period where the informed firms raise their prices just a little: through this mild price increase, these firms forward their signal to the uninformed firms, and they do so in a credible way, as this makes the actual consumers’ status common knowledge. Instead, a sudden price jump already in the first period is not sustainable as an equilibrium. We also show how our results extend to a duopoly market with differentiated products.
Chillemi et al. (2026) studied this question.