Infinite Horizon Nash Equilibrium Models of a Limit Order Book

The paper analyzes some models of a Limit Order Book, determined as a Nash equilibrium among a large number of traders, in infinite time horizon. We study how the size and shape of the LOB are related to the expected profit rate of traders posting limit orders, and to the random distribution of incoming external buy or sell orders. Formulas are derived which show how the volatility of the stock, and the presence of better informed external agents, determine (i) an increase in the bid-ask spread and (ii) a liquidity reduction, i.e. a decrease in the total amount of stocks posted for purchase or for sale. We also analyze models including “fast” and “slow” traders, that can react more or less quickly to changes in the fundamental value of the stock.