Who provides liquidity, and when?

We model competition for liquidity provision between high-frequency traders (HFTs) and slower execution algorithms (EAs) designed to minimize investors’ transaction costs. Under continuous pricing, EAs dominate by using aggressive limit orders stimulate HFTs’ market orders. discrete HFTs if the bid-ask spread is binding at one tick. If tick size (minimum price variation) not binding, choose stimulating providing non-HFTs. Transaction costs increase with but can be negatively correlated when all provide liquidity.