A Lagrangian approach to constrained potential games

Theory and examples

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

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.

Original languageEnglish (US)
Title of host publicationProceedings of the 47th IEEE Conference on Decision and Control, CDC 2008
Pages2420-2425
Number of pages6
DOIs
StatePublished - 2008
Event47th IEEE Conference on Decision and Control, CDC 2008 - Cancun, Mexico
Duration: Dec 9 2008Dec 11 2008

Other

Other47th IEEE Conference on Decision and Control, CDC 2008
CountryMexico
CityCancun
Period12/9/0812/11/08

Fingerprint

Potential Games
Game theory
Potential Theory
Game Theory
Power control
Game
Non-cooperative Game
Rate Control
Power Control
Nash Equilibrium
Simplify
Duality
Existence and Uniqueness
Engineering
Necessary
Optimization
Sufficient Conditions

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

Cite this

Zhu, Q. (2008). A Lagrangian approach to constrained potential games: Theory and examples. In Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008 (pp. 2420-2425). [4738596] https://doi.org/10.1109/CDC.2008.4738596

A Lagrangian approach to constrained potential games : Theory and examples. / Zhu, Quanyan.

Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008. 2008. p. 2420-2425 4738596.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Zhu, Q 2008, A Lagrangian approach to constrained potential games: Theory and examples. in Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008., 4738596, pp. 2420-2425, 47th IEEE Conference on Decision and Control, CDC 2008, Cancun, Mexico, 12/9/08. https://doi.org/10.1109/CDC.2008.4738596
Zhu Q. A Lagrangian approach to constrained potential games: Theory and examples. In Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008. 2008. p. 2420-2425. 4738596 https://doi.org/10.1109/CDC.2008.4738596
Zhu, Quanyan. / A Lagrangian approach to constrained potential games : Theory and examples. Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008. 2008. pp. 2420-2425
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