Game　semantics　is　suitable　to　model　interactions　between　the　environment　(modeled　as　opponent　role)　and　the　system　(modeled　as　player　role),　and　has　gained　great　successes　in　which　the　behaviors　of　the　system　and　the　environment　are　explicitly　distinguished.　In　this　paper,　game　semantics　model　(exactly　asynchronous　game)　is　introduced　into　the　actors　which　is　called　ActorGame.　The　characteristics　of　actor　computation　model,　such　as　receiving　messages,　sending　messages　and　creating　new　actors,　are　well　interpreted　in　ActorGame.　And　also　composition　of　ActorGames　and　category　of　ActorGames　are　concerned.　Both　the　ActorGame,　composition　of　ActorGames,　and　category　of　ActorGames　have　good　properties.