A computer game is usually considered as a finite state machine. For a distributed multiplayer game, state information has to be exchanged among its players when they move and interact in a virtual space. If the number of players is very large, only a small subset of the game entities, controlled by their players, is interested and forms a multicast group so as to reduce the information dissemination over the network. In this paper, analytical models are proposed for evaluating the performance of multicast groups with multiplayer games in peer-to-peer networks. The system modeling is based on two stochastic processes and their possible solutions in terms of game type, player activity, and entity vision size, mode of user input processing, and grouping strategy. The cost of game operations on consumed resources is introduced to characterize the performance measure. Numerical examples are demonstrated, which provide useful insights of the behaviors of such systems.