Order　execution　is　an　important　operational　level　of　activity　encountered　in　portfolio　investment　and　risk　management.　We　study　a　sequential　Stackelberg　order　execution　game　which　arises　naturally　from　the　practice　of　algorithm　trading　in　financial　markets.　The　game　consists　of　two　risk-neutral　traders,　one　leader　and　one　follower,　who　compete　to　maximize　their　expected　payoffs　respectively　by　trading　a　single　risky　asset　whose　price　dynamics　follows　a　linear-price　market　impact　model　over　a　finite　horizon.　This　new　Stackelberg　game　departs　from　the　Nash　games　which　have　been　the　main　focus　in　the　algorithm　trading　literature.　We　derive　a　closed-form　solution　for　the　unique　open-loop　Stackelberg　equilibrium　by　exploiting　the　special　structures　of　the　model.　This　analytic　solution　enables　us　to　develop　new　and　complementary　managerial　insights　by　looking　at　both　players＇　equilibrium　behavior　in　terms　of　trading　speeds　and　positions,　expected　price　dynamics,　price　of　anarchy,　first　mover＇s　advantage,　and　trading　horizon　effect.