New insights on generalized nash games with shared constraints: Constrained and variational equilibria

Ankur A. Kulkarni, Vinayak V. Shanbhag

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

6 Scopus citations

Abstract

We consider generalized noncooperative Nash games with "shared constraints" in which there is a common constraint that players' strategies are required to satisfy. We address two shortcomings that the associated generalized Nash equilibrium (GNE) is known to have: (a) shared constraint games usually have a large number (often a manifold) of GNEs and (b) the GNE may not be the appropriate solution concept for exogenously imposed constraints. For (a), we seek a refinement of the GNE and study the variational equilibrium (VE), defined by [1], [2], as a candidate. It is shown that the VE and GNE are equivalent in a certain degree theoretic sense. For a class of games the VE is shown to be a refinement of the GNE and under certain conditions the VE and GNE are observed to coincide. To address (b), a new concept called the constrained Nash equilibrium (CNE) is introduced. The CNE is an equilibrium of the game without the shared constraint that is feasible with respect to this constraint. Sufficient conditions for the existence of a CNE are derived and relationships with the GNE and VE are established.

Original languageEnglish (US)
Title of host publicationProceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009
Pages151-156
Number of pages6
DOIs
StatePublished - Dec 1 2009
Event48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 - Shanghai, China
Duration: Dec 15 2009Dec 18 2009

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0191-2216

Other

Other48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009
CountryChina
CityShanghai
Period12/15/0912/18/09

All Science Journal Classification (ASJC) codes

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

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    Kulkarni, A. A., & Shanbhag, V. V. (2009). New insights on generalized nash games with shared constraints: Constrained and variational equilibria. In Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 (pp. 151-156). [5399507] (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2009.5399507