Monotonic Generalized Nash Games with Application to the Management of Energy-Aware Aloha Networks

Generalized Nash games differ from strategic form games by allowing the strategy set available for each player to depend on the strategies selected by the other players. The strong dependence of the strategies of the players make these generalized games harder to analyze. While convex generalized games are well understood, the case where the constraint sets and rewards are non-convex is significantly more complicated. In this paper we analyze a family of monotonic generalized games (not necessarily convex). We provide uniqueness and existence theorems for these games as well as rapidly converging algorithm for obtaining a Nash equilibrium. We then use the proposed solution to optimize access probability and energy consumption in ALOHA networks, where users have fixed but heterogeneous QoS requirements.