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A Lagrangian approach to constrained potential games: Theory and examples

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1 Author(s)
Quanyan Zhu ; Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, USA, 61820

In this paper, we use a Lagrangian approach to solve for Nash equilibrium in a continuous non-cooperative game with coupled constraints. We discuss the necessary and the sufficient conditions to characterize the equilibrium of the constrained games. In addition, we discuss the existence and uniqueness of the equilibrium. We focus on the class of potential games and point out a relation between potential games and centralized optimization. Based on these results, we illustrate the Lagrangian approach with symmetric quadratic games and briefly discuss the notion of game duality. In addition, we discuss two engineering potential game examples from network rate control and wireless power control, for which the Lagrangian approach simplifies the solution process.

Published in:

Decision and Control, 2008. CDC 2008. 47th IEEE Conference on

Date of Conference:

9-11 Dec. 2008