We model high-frequency traders in electronic markets. We ask how the presence of such middlemen may affect welfare. We find that middlemen process public information faster than the average investor. As such, they can play a positive or a negative role. On the positive side, when they enter a...

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...

A limit order market enables an early seller to trade with a late buyer by leaving a price quote. Information arrival in the interim period creates adverse selection risk for the seller and therefore hampers trade. Entry of high-frequency traders (HFTs) might restore trade as their machines can...