An evolutionary game theoretic framework for coexistence in Cognitive Radio Networks

Cognitive Radio Networks (CRN) employ coexistence protocols for spectrum sharing when collocated in a given region. Existing coexistence protocols do not take into consideration the fact that available spectrum bands vary significantly in their characteristics and quality they provide which makes some channels of the spectrum more attractive than others. In this paper, we analyze this situation from an evolutionary game theoretic perspective and show how CRNs would evolve their strategies of contending for disparate spectrum resources. We derive the equilibrium state for CRNs´ spectrum sharing game and show that the population mix in equilibrium cannot be invaded by a mutant strategy which is greedier than the incumbent strategy and is therefore an evolutionarily stable strategy (ESS). We also derive the replicator dynamics of the proposed evolutionary game which represent how players learn from payoff outcomes of their strategic interactions and modify their strategies at every stage of the game. Since all players approach the ESS based solely on the common knowledge payoff observations, the evolutionary game can be implemented in a distributed manner. Simulation results show that the replicator dynamics enable strategic choices of CRNs to converge to ESS and also make them robust against changing network conditions.