Non-Reservation Price Equilibria and Search Without Priors

In this paper we analyse a model of oligopolistic competition in which consumers search without priors. Consumers do not have prior beliefs about the distribution of prices charged by firms and thus try to use a robust search procedure: they minimise the loss relative to the searcher, who knows the price distribution, in the worst case scenario. We derive the optimal stopping rule and show that it does not possess the reservation price property. This means that for a range of prices for which consumers stop searching with a probability strictly between zero and one. We show that for any distribution of search costs there is a unique market equilibrium characterised by price dispersion. Therefore search without priors helps resolve the famous Diamond (1971) paradox. We show that although listed prices approach the monopoly price as the number of firms increases, the effective price paid by consumers does not depend on the number of firms. We show that prices in our model are lower than those in a model where consumers know the distribution of prices. The reason is that consumers actively search in equilibrium, and this pushes prices down. This effect is so strong that the price decrease more than compensates consumers for their extra search costs