Price-directed search and collusion

In many (online) markets, consumers can readily observe prices, but need to examine individual products at positive cost in order to assess how well they match their needs. We propose a tractable model of price-directed sequential search in a market where firms compete in prices. Each product meets consumers' basic needs, however they are only fully satisfied with a certain probability. In our setup, four types of pricing equilibria emerge, some of which entail inefficiencies as not all consumers are (always) served. We then lend our model to analyze collusion. We find that for any number of firms, there exists a parameter region in which the payoff-dominant symmetric collusive equilibrium gives rise to a higher expected total social welfare than the repeated one-shot Nash equilibrium. In other regions, welfare is identical under collusion and merely consumer rents are transferred, or both welfare and consumer rents are reduced. An all-inclusive cartel maximizing industry profit increases welfare for an even larger set of parameters, but may also be detrimental to it.