—A major contribution of biology to competitive decision making is the area of evolutionary games. It describes the evolution of sizes of large populations as a result of many local interactions, each involving a small number of randomly selected individuals. An individual plays only once; it plays in a one shot game against another randomly selected player with the goal of maximizing its utility (fitness) in that game. We introduce here a new more general type of games: a Stochastic Evolutionary Game where each player may be in different states; the player may be involved in several local interactions during his life time and his actions determine not only the utilities but also the transition probabilities and his life duration. This is used to study a large population of mobiles forming a sparse ad-hoc network, where mobiles compete with their neighbors on the access to a radio channel. We study the impact of the level of energy in the battery on the aggressiveness of the access policy of mobiles at equilibrium. We obtain properties of the ESS (Evolutionary Stable Strategy) equilibrium which, Unlike the Nash equilibrium concept, is robust against deviations of a whole positive fraction of the population. We further study dynamical properties of the system when it is not in equilibrium.