An　independent　set　game　is　a　cooperative　game　dealing　with　profit　sharing　in　the　maximum　independent　set　problem.　A　population　monotonic　allocation　scheme　is　a　rule　specifying　how　to　share　the　profit　of　each　coalition　among　its　participants　such　that　every　participant　is　better　off　when　the　coalition　expands.　In　this　paper,　we　provide　a　necessary　and　sufficient　characterization　for　independent　set　games　admitting　population　monotonic　allocation　schemes.　Moreover,　our　characterization　can　be　verified　efficiently.　©　2022　Elsevier　B.V.