Maintaining　a　consistent　persona　is　essential　for　building　a　human-like　conversational　model.　However,　the　lack　of　attention　to　the　partner　makes　the　model　more　egocentric:　they　tend　to　show　their　persona　by　all　means　such　as　twisting　the　topic　stiffly,　pulling　the　conversation　to　their　own　interests　regardless,　and　rambling　their　persona　with　little　curiosity　to　the　partner.　In　this　work,　we　propose　COSPLAY(COncept　Set　guided　PersonaLized　dialogue　generation　Across　both　partY　personas)　that　considers　both　parties　as　a　＂team＂:　expressing　self-persona　while　keeping　curiosity　toward　the　partner,　leading　responses　around　mutual　personas,　and　finding　the　common　ground.　Specifically,　we　first　represent　self-persona,　partner　persona　and　mutual　dialogue　all　in　the　concept　sets.　Then,　we　propose　the　Concept　Set　framework　with　a　suite　of　knowledge-enhanced　operations　to　process　them　such　as　set　algebras,　set　expansion,　and　set　distance.　Based　on　these　operations　as　medium,　we　train　the　model　by　utilizing　1)　concepts　of　both　party　personas,　2)　concept　relationship　between　them,　and　3)　their　relationship　to　the　future　dialogue.　Extensive　experiments　on　a　large　public　dataset,　Persona-Chat,　demonstrate　that　our　model　outperforms　state-of-the-art　baselines　for　generating　less　egocentric,　more　human-like,　and　higher　quality　responses　in　both　automatic　and　human　evaluations.　©　2022　ACM.