We study a dynamic limit order market with a finite number of strategic liquidity suppliers who post limit orders. Their limit orders are hit by either news (i.e. informed) traders or noise traders.
We show that repeatedly playing a mixed strategy equilibrium of a certain static game is a subgame perfect equilibrium with fleeting orders and flickering quotes. Furthermore, regardless of the distributions of the liquidation value and noise trade quantity, we always find a sequence of equilibria in mixed strategies such that the resulting random supply schedule converges in mean square, as the number of liquidity suppliers increases to infinity, to the deterministic competitive supply function.