Rational Buyers Search When Prices Increase

We develop a dynamic pricing model motivated by observed patterns in business-to-business (and some business-to-customer) transactions. Seller costs are perfectly correlated and evolve according to a Markov process. In every period, each buyer observes (for free) the price set by their current supplier, but not the other sellers' prices or the sellers' (common) cost level. By paying a cost s the buyer becomes "active" and benefits from (Bertrand) competition among sellers. We show that there exists a semi-separating equilibrium whereby sellers increase price immediately when costs increase and otherwise decrease price gradually. Moreover, buyers become active when prices increase but not otherwise. In sum, we deliver a theory whereby buyers become active ("search") if and only if their supplier increases price.