Equilibrium in a Dynamic Limit Order Market

We model a dynamic limit order market as a stochastic sequential game. Since the model is analytically intractable, we provide an algorithm based on Pakes McGuire (2001) to find a stationary equilibrium, we generate artifical time series and perform comparative dynamics. As we know the data generating process, we can compare transaction prices to the true value of the asset, as well as explicitly determine the welfare gains accruing to investors. Due to the endogeneity of order flow, the midpoint of the quoted price is not a good proxy for the true value. Further, transaction costs paid by market order submitters are negative on average. As a policy experiment we consider the effect of a reduction in tick size, and find that it has a positive impact on investor surplus.