Abstract
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 liquidity provision by using aggressive limit orders to stimulate HFTs' market orders. Under discrete pricing, HFTs dominate liquidity provision if the bid-ask spread is binding at one tick. If the tick size (minimum price variation) is not binding, EAs choose between stimulating HFTs and providing liquidity to non-HFTs. Transaction costs increase with the tick size but can be negatively correlated with the bid-ask spread when all traders can provide liquidity