Mean-Field Games for Resource Sharing in Cloud-Based Networks

In this paper, we consider last level cache (LLC) sharing problems in large-scale cloud networks with a fair payoff function. We formulate the problem as a strategic decision-making problem (i.e., a game). We examine the resource-sharing game with finite and infinite number of players. Exploiting the aggregate structure of the payoff functions, we show that the resource-sharing game has a Nash equilibrium in a wide range of return index. We show that the Nash equilibrium is not an evolutionarily stable strategy in the finite regime. Then, we introduce a myopic mean-field response where each player implements a mean-field-taking strategy. We show that such a mean-field-taking strategy is an evolutionarily stable strategy in both finite and infinite regime. We provide closed-form expression of the optimal pricing that gives an efficient resource-sharing policy. As the number of active players grows without bound, we show that the equilibrium strategy converges to a mean-field equilibrium, and the optimal prices for resources converge to the optimal price of the mean-field game. Then, we address the demand satisfaction problem for which a necessary and sufficient condition for satisfactory solutions is provided. In addition, a very fast mean-field learning algorithm is provided.