Non-Alternating ActorGame: Game semantics for actors without alternation

Based on the works of ActorGames which introduce game semantics into actors, we remove the assumption of an immediate acknowledgement to a received message for an actor in ActorGames. This makes ActorGames play without alternation and a new kind of game semantics called Non-Alternating ActorGames are introduced. Through an example of classical cluster computing called CCC and implemented by actors, we analyze the concurrent messages among actors and introduce the Non-Alternating ActorGame strategy, composition of Non-Alternating ActorGames, the Non-Alternating ActorGame category and relation to concurrent games. Both the Non-Alternating ActorGame strategy, composition of Non-Alternating ActorGames, the Non-Alternating ActorGame category and relation to concurrent games have good properties.