This paper provides a game theoretic model of price formation and order placement decisions in a dynamic limit order market. Investors can choose to post limit orders or to submit market orders. Limit orders result in better execution prices but face a risk of non-execution and a winner’s curse problem. The execution probability of a limit order trader is endogenous and depends on the order placement decisions of the other traders. Solving for the equilibrium of this dynamic game, closed form solutions for the order placement strategies are obtained. Thus, testable implications for the cross-sectional behaviour of the mix between market and limit orders and trading costs in limit order markets are derived. It is also shown that the winner’s curse problem has a negative impact on the allocative efficiency of these markets.