Structural Solutions for Additively Coupled Sum Constrained Games

We propose and analyze a new family of games played by resource-constrained players. In particular, each strategic user has a single sum resource constraint over its action space and its own action impacts its own payoff through additive combinations of the other users' actions. We investigate convergence properties of various solutions for these games with and without real-time information exchange. First, when users cannot exchange messages with each other, but desire to maximize their individual utilities, we derive sufficient conditions under which best response dynamics converges to a globally asymptotically stable Nash equilibrium. Second, when users can exchange price signals in real-time to achieve coordination, we also establish the convergence properties of two action update mechanisms, including gradient play and Jacobi update. The investigated game model and our proposed solutions are readily applicable to various multi-user interaction, including communication networking applications, such as power control and flow control.