A Market-Clearing Role for Inefficiency on a Limit Order Book

Abstract

Using a stochastic sequential game, this paper models limit order book trading dynamics. It deduces ex ante surplus and some agents' strategies by using an intuitive stationarity property of equilibrium. This largely bypasses any need for direct analysis of agents' (traders') intricate forecasting problems. Surplus per agent, while decreasing in the bid-ask spread, is invariant to some interesting dynamic features of the model. One interpretation of this is that market inefficiency is fixed by the spread at a 'liquidity market-clearing' level. The model best describes cases where price-discreteness leads to a mainly-constant spread. Here, a smaller price tick size raises surplus, and is to be encouraged.

Keywords: stochastic sequential game, ergodic equilibrium, market microstructure, limit order book, market depths, bid-ask spread

JEL Classification: C73, G14, G24