Evolutionary coalitional games for random access control

In this paper we consider a random access system where each user can be in two modes of operation, has a packet or not and the set of users which have a packet is available to a shared medium. We propose an evolving coalitional game theory to analyze the system outcomes. Unlike classical coalitional approaches that assume that coalitional structures are fixed and formed with cost-free, we explain how coalitions can be formed in a fully distributed manner using evolutionary dynamics and coalitional combined fully distributed payoff and strategy (CODIPAS) learning. We introduce the concept of evolutionarily stable coalitional structure (ESCS), which is, when it is formed it is resilient by small perturbation of strategies. We show that (i) the formation and the stability of coalitions depend mainly on the cost of making a coalition compared to the benefit of cooperation, (ii) the grand coalition can be unstable and a localized coalitional structure is formed as an evolutionarily stable coalitional structure. When the core is empty, the coalitional CODIPAS scheme selects one of the stable sets. Finally, we discuss the convergence and complexity of the proposed coalitional CODIPAS learning in access control with different users' activities.