An Extension of Duality and Hierarchical Decomposition to a Game-Theoretic Framework

This paper extends some duality results from a standard optimization setup to a noncooperative (Nash) game framework. A coupled constrained Nash game is considered. Solving directly such a coupled Nash game requires coordination among possibly all players. An alternative approach is proposed based on the equivalence to a special constrained optimization problem for an NG-game cost function. By exploiting specific separability properties of the NG-game cost, this duality approach leads to a natural hierarchical decomposition into a lower-level uncoupled Nash game and a higher-level system optimization problem.