Stable Nash equilibria of medium access games under symmetric, socially altruistic behavior

We consider the effects of altruistic behavior on random medium access control (slotted ALOHA) for local area communication networks. For an idealized, synchronously iterative, two-player game with asymmetric player demands, we find a Lyapunov function governing the “better-response” Jacobi dynamics under purely altruistic behavior. Though the positions of the interior Nash equilibrium points do not change in the presence of altruistic behavior, the nature of their local asymptotic stability does. There is a region of partially altruistic behavior for which both interior Nash equilibrium points are locally asymptotically stable. Variations of these altruistic game frameworks are discussed considering power (instead of throughput) based costs and linear utility functions. Also, for a power control game with a single Nash equilibrium, we show how its stability changes as a function of the altruism parameter.