Public Information and Sequential Learning in a Bilateral Market

Abstract

I study the effects of improved public information on equilibrium welfare and price dispersion, providing sufficient conditions for negative and positive effects. Public information affects welfare by reducing excessive (though rational) pessimism induced by sequential learning. Reduced pessimism results in fewer agents withdrawing from the market prematurely (compared with the full information benchmark), which increases own ex-post utility in expectation but may also cause a congestion externality. I show that either effect can dominate. Observed search duration on the short side of the market is an indicator of the welfare effects of public information. The context is a search, matching and bargaining market with uncertainty about the meeting probability on both sides. Fully rational, ex-ante identical participants gather private information endogenously through costly search. Full trade is the unique perfect Bayesian equilibrium under general conditions. Full trade implies learning terminates following a positive but not following a negative signal, which results in a declining belief path and in declining reservation prices during search. The results hold for any prior distribution where a more precise public signal slows learning.