Large Orders in Small Markets: On Optimal Execution with Endogenous Liquidity Supply
We solve a Stackelberg game where a large uninformed seller executes optimally, fully cognizant of the response of Cournot-competitive market makers. The game therefore endogenizes both demand and supply of liquidity. The closed-form solution yields several insights. First, stealth trading is both privately and socially costly because market makers incur additional cost not knowing when execution ends. Second, the presence of a large seller does not unambiguously benefit other participants. Market makers benefit only if there is enough risk-absorption capacity or if the execution period is short. Other investors benefit only when the seller sells at high enough intensity.