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

TL;DR

This paper investigates how altruistic behavior influences the stability of Nash equilibria in medium access control games, revealing that altruism can alter equilibrium stability and lead to regions with unstable equilibria.

Contribution

It introduces a Hamiltonian framework for analyzing altruistic effects on Nash equilibria stability in medium access games, extending understanding of altruism's impact on network game dynamics.

Findings

Interior Nash equilibrium positions remain unchanged with altruism.

Altruism can destabilize equilibria, creating regions with no stable interior points.

Stability of power control games varies with altruism levels.

Abstract

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 Hamiltonian governing the 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 neither interior Nash equilibrium point is locally asymptotically stable. Also, for a power control game with a single Nash equilibrium, we show how its stability changes as a function of the altruism parameter. Variations of these altruistic game frameworks are discussed considering power (instead of throughput) based costs and linear utility functions.