We consider in this paper dynamic Multiple Access (MAC) games between a random number of players competing over collision channels. Each of several mobiles involved in an interaction determines whether to transmit at a high or at a low power. High power decreases the lifetime of the battery but results in smaller collision probability. We formulate this game as an anonymous sequential game with undiscounted reward which we recently introduced and which combines features from both population games (infinitely many players) and stochastic games. We briefly present this class of games and basic equilibrium existence results for the total expected reward as well as for the expected average reward. We then apply the theory in the MAC game.