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

Jeremy Large, All Souls College, University of Oxford


Abstract

Using a stochastic sequential game in ergodic equilibrium, this paper models
limit order book trading dynamics. It deduces investor surplus and some
agents' strategies from depth's stationarity, while bypassing altogether
agents' intricate forecasting problems. Market inefficiency adjusts to
induce equal supply and demand for liquidity over time. Consequently, at a
given bid-ask spread surplus per investor is invariant to faster, more
regular or more sophisticated trading, or modified queuing rules: apparent
improvements are offset as inefficiency adjusts back to market-clearing
levels. Moreover, investor surplus decreases with the spread. In the model,
price discreteness fixes the spread at the tick size. Narrowing the tick is
beneficial, but may be resisted by sell-side traders.

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

JEL classification: C73, G14, G24