Game theoretic considerations for the Gaussian Multiple Access Channel

We study the behavior of users in a classical Additive White Gaussian Noise Multiple Access Channel. We model users as rational entities whose only interest is to maximize their own communication rate, and we model their interaction as a noncooperative one-shot game. The Nash equilibria of the two-user game are found, and the relation between the pure-strategy and mixed-strategy Nash equilibria is discussed. As in most games, the absence of cooperation and coordination leads to inefficiencies.We then extend our setting using evolutionary game theory, which we use to model a large population of users playing the MAC game over time. A unique evolutionary stable strategy is found for this case, corresponding to the strategy achieving the Nash equilibrium in a simplified one-shot game. Finally, we investigate what happens to the distribution of strategies in a population when we assume that the number of offsprings of a user is equal to the payoff of this user in a one-shot game. We find that the system converges to a state in which the average strategy of the population is the evolutionary stable strategy.