Equilibrium Bid-Price Dispersion

Abstract

If bidding in a common-value auction is costly and if bidders do not know how many others are also bidding, all equilibria are in mixed strategies. Participation is probabilistic and bid prices are dispersed. The symmetric equilibrium is unique and yields simple analytic expressions. We use them to, for example, show that bid prices exhibit negative skew. The expressions are further used to estimate the model based on bidding in an S&P500 security. We find that the number of bidders declined over time, making liquidity supply fragile. A similar trend emerges when zooming in on the Flash Crash.