Decentralized trading with private information

We characterize an environment in which agents have private information and trade in decentralized markets. First, we show that all the useful information is learned in the long run. Second, we show that agents with private information receive rents, and the value of information is positive. This is in contrast to the classic analysis of Grossman and Stiglitz (1980) who show that in centralized markets with private information, the value of information is zero. Finally, we show that equilibrium allocations are efficient in the long run. We also provide characterization of the connection of volume to prices of assets.