Despite the lack of delegated monitor and of collateral guarantees P2P lending platforms exhibit relatively low loan and delinquency rates. The adverse selection is indeed mitigated by a new screening technology (information processing through machine learning) that provides costless public signals. Using data from Prosper and Lending Club we show that loans' spreads, proxing asymmetric information, decline with credit scores or hard information indicators and with indications from "group ties" (soft information from social networks). Also an increase in the risk of bank run in the traditional banking sector increases participation in the P2P markets and reduces their rates (substitution effect). We rationalize this evidence with a dynamic general equilibrium model where lenders and borrowers choose between traditional bank services (subject to the risk of bank runs and early liquidation) and P2P markets (which clear at a pooling price due to asymmetric information, but where public signals facilitate screening). JEL codes: G11, G23. Keywords: peer-to-peer lending, pooling equilibria, signals, value of information, liquidity shocks.