Two Firms is enough for Competition, but Three or More is better

We present an oligopoly model where a certain fraction of consumers engage in costly non-sequential search to discover prices. There are three distinct price dispersed equilibria characterized by low, moderate and high search intensity, respectively. We show that the effects of an increase in the number of firms active in the market are sensitive (i) to the equilibrium consumers' search intensity, and (ii) to the status quo number of firms. For instance, when consumers search with low intensity, increased competition does not affect expected price, leads to greater price dispersion and welfare declines. In contrast when consumers search with high intensity, increased competition results in lower prices when the number of competitors in the market is low to begin with, but in higher prices when the number of competitors is large. Moreover, duopoly yields identical expected price and price dispersion but higher welfare than an infinite number of firms.