Recently the control of multi-agent behavior using two-player non-zero sum games, such as prisoner's dilemma, has been studied. In this paper we propose a two player game that includes a dilemmatic structure and extend it to the study of two teams consisting of many players. Iterative versions of dilemma games have been investigated extensively and many strategies for the games have been proposed. For multi-agent applications we extend our dilemma game to a multi-player version. Several decision strategies are studied with this model. The multi-player model is used to decide actions of agents in the burden carriage problem, which includes a typical situation of agents in competition. We show that the behavior of agents in the problem matches the results of team contests of the dilemma game.