Aggregate uncertainty and learning in a search model

We show that there exists a unique equilibrium in monotone strategies. We characterize equilibrium behavior for given levels of frictions. We show that new buyers experiment with low bids initially. Over time, the fact that the buyer is loosing provides bad news about the state of the world, revealing that there are many competing buyers. Consequently, the buyer becomes more pessimistic and bids more aggressively. The resulting equilibrium bid pattern is monotone increasing in the buyer's search duration. Different from most existing models of search with learning, in our model, the price distribution (the distribution of competing bids) is endogeneous and depends on the level of frictions. Interestingly, lower frictions are not necessarily beneficial for buyers. While lower search frictions make search less costly, the price distribution can be much worse with lower frictions. We show that, indeed, expected equilibrium payoffs may be non-monotone in the level of search frictions. Finally we show that, as search frictions vanish, the equilibrium allocation converges to the competitive allocation. Thus, the decentralized search market aggregates dispersed information and the resulting equilibrium trading price reveals the state.