Evolutionary game dynamics with migration for hybrid power control in wireless communications

We propose an evolutionary game dynamics with migration for hybrid population games with many local interactions at the same time. Each local interaction concerns a random number of interacting players. The strategies of a player have two components. Specifically, each player chooses both (i) the region or subpopulation and (ii) an action among a finite set of secondary pure strategies in each region. We assume that when updating a strategy, a player can change only the secondary strategies associate to the region at a time. We investigate what impact this restriction has on the population dynamics. We apply this model to the integrated power control and base station assignment problem in a multi-cell in code division multiple access (CDMA) wireless data networks with large number of mobiles. We show that global neutrally evolutionary stable strategies are stationary points of hybrid mean dynamics called dynamics with multicomponent strategies under the positive correlation conditions. We give some convergence results of our hybrid model in stable population games and potential population games.