An extension of duality to a game-theoretic framework

Authors:
Lacra Pavel
Affiliations:
Department of Electrical and Computer Engineering, University of Toronto, Toronto, ON, Canada M5S 3G4
Venue:
Automatica (Journal of IFAC)
Year:
2007

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Abstract

This paper extends some duality results from a standard optimization setup to a noncooperative (Nash) game framework. A Nash game (NG) with coupled constraints is considered. Solving directly such a coupled NG requires coordination among possibly all players. An alternative approach is proposed based on its relation to a special constrained optimization problem for the NG-game cost function, with respect to the second argument that admits a fixed-point solution. Specific separability properties of the NG-game cost are exploited and duality results are developed. This duality extension leads naturally to a hierarchical decomposition into a lower-level NG with no coupled constraints, and a higher-level system optimization problem. In the second part of the paper these theoretical results are applied to a coupled NG with coupled constraints as encountered in optical networks.