A control theoretic approach to noncooperative game design

This paper investigates design of noncooperative games from a control theoretic perspective. Pricing mechanisms are used as a design tool to ensure that the Nash equilibrium of a broad class of noncooperative games satisfies certain global objectives such as welfare maximization. The class of games considered provide a theoretical basis for a variety of decentralized resource allocation and control problems including network congestion control, wireless uplink power control, and optical power control. The game design problem is analyzed under full and limited information assumptions for dynamic systems and nonseparable utility functions. Stability properties of the game and pricing dynamics are studied under the assumption of timescale separation and in two separate time-scales. Thus, sufficient conditions are derived, which allow the designer to place the Nash equilibrium solution or to guide the system trajectory to a desired region or point. The obtained results are illustrated with examples.