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

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.