The strategic specialist and imperfect competition in a limit order market

The empirical literature suggests that the limit order book contains information that might be used by the specialist to his own advantage. I develop a model where there is a strategic specialist who competes against a limit order book and has information about supply. The presence of a strategic specialist in an imperfectly competitive limit order book market induces non-monotonicity of market indicators with respect to the variance of liquidation value. Moreover, the existence of private information about supply significantly affects market performance as it induces, among other effects, lower market liquidity. Finally, this model suggests another link between Kyle's (1985, 1989) [Kyle, A., 1985. Continuous auctions and insider trading. Econometrica 53, 1315-1336, Kyle, A., 1989. Informed speculators with imperfect competition. Review of Economic Studies 56, 317-356] and Glosten and Milgrom's (1985) [Glosten, L., Milgrom, P., 1985. Bid, ask and transaction prices in a specialist market with heterogeneously informed markets. Journal of Financial Economics 14, 71-100] models by allowing for strategic behaviour of the specialist.