On convexity and monotonicity in generalized aggregative games

Large-scale multi-agent systems arise in several control applications, such as demand side management in smart power networks, traffic control in intelligent transportation systems, and congestion control in communication networks. All these systems comprise a large population of noncooperative agents whose decision making process can be modeled as a generalized aggregative game. In this paper, we analyze the usual convexity assumption and the monotonicity of the so-called game mapping. Specifically, we show necessary and sufficient conditions on the problem data such that monotonicity holds. The derived conditions show that monotonicity cannot be expected in general.