Mean-field Game Approach to Admission Control of an M/M/∞\infty Queue with Decreasing Congestion Cost

International audienceWe study a mean field approximation of the M/M/$\infty$ queuing system. This queue is often used to model the number of cellular phone users in a cell. We assume that congestion here has a positive impact on the performance so that the more there are users, the less it is costly to offer a service per cell phone, for example, if a base station broadcasts a film then the cost per customer decreases. We obtain closed-form formulas for the equilibria. We show that the mean-field approximation becomes tight as the workload increases, thus the results obtained for the mean-field model well approximate the discrete one

From mean field interaction to evolutionary game dynamics

International audienceWe consider evolving games with finite number of players, in which each player interacts with other randomly selected players. The types and actions of each player in an interaction together determine the instantaneous payoff for all involved players. They also determine the rate of transition between type-actions. We provide a rigorous derivation of the asymptotic behavior of this system as the size of the population grows. We show that the large population asymptotic of the microscopic model is equivalent to a macroscopic evolutionary game in which a local interaction is described by a single player against an evolving population profile. We derive various classes of evolutionary game dynamics. We apply these results to spatial random access games in wireless networks