Oligopolistic competition and search without priors

I study a model of oligopolistic competition in which consumers search for prices, but have no idea about the underlying price distribution. Consumers’ behaviour satisfies four consistency requirements such that beliefs about the underlying distribution maximize Shannon entropy. I derive the optimal stopping rule and equilibrium price distribution of the model. Unlike in Stahl (1989), the expected price is decreasing in the number of firms. Moreover, consumers can benefit from being uninformed, if the number of firms is sufficiently large.