As　an　environmentally　friendly　and　convenient　transport　mode,　bike-sharing　has　been　fast　developed　in　major　cities　around　the　world.　More　bike-sharing　firms　have　been　formed　and　intensified　market　competition.　The　government　has　stipulated　regulations　to　intervene　in　bike-sharing　firm　operations　and　to　maintain　orderly　competition.　This　paper　establishes　an　integrated　economic　model　to　examine　duopoly　bike-sharing　firm　competition　in　both　prices　and　the　number　of　deployed　bikes.　Specifically,　more　deployed　bikes　in　the　urban　area　reduce　the　time　cost　for　the　users　to　find　an　available　bike　(i.e.,　the　search　cost),　but　they　can　also　impose　a　negative　social　externality　on　the　urban　management.　Two　government　policies　to　control　the　number　of　deployed　bikes　have　been　examined　and　benchmarked.　One　is　the　limit　on　the　total　number　of　the　deployed　bikes　(i.e.,　the　supply-side　regulation),　and　the　other　is　the　restriction　to　allow　the　users　to　only　register　or　use　certain　firms’　services　(i.e.,　the　demand-side　regulation　of　single-homing).　Our　model　is　also　further　calibrated　by　using　the　bike-sharing　market　data　of　Beijing　for　policy　implications.　It　is　found　that,　when　the　negative　social　externality　of　bike　deployment　is　sufficiently　small,　the　government　should　allow　users’　multi-homing　(i.e.,　registration　on　both　firms’　platforms).　However,　when　the　negative　social　externality　is　high,　the　government　should　strictly　control　the　number　of　bikes　through　both　the　supply-side　and　demand-side　restrictions.　Our　analyses　also　suggest　that　it　is　never　socially　optimal　to　only　adopt　the　demand-side　restriction　(i.e.,　forcing　the　single-homing).　That　is,　the　supply-side　policy　is　more　socially　preferred　to　correct　the　negative　social　externality　in　most　cases.　When　two　bike-sharing　firms　offer　quite　heterogeneous　services　(i.e.,　low　service　substitutability),　it　is　more　socially　optimal　to　only　implement　the　supply-side　policy.　©　2023　Elsevier　Ltd