Nash equilibrium problems with congestion costs and shared constraints

Huibing Yin, Vinayak V. Shanbhag, Prashant G. Mehta

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

7 Citations (Scopus)

Abstract

Generalized Nash equilibria (GNE) represent extensions of the Nash solution concept when agents have shared strategy sets. This generalization is particularly relevant when agents compete in a networked setting. In this paper, we consider such a setting and focus on a congestion game in which agents contend with shared network constraints. We make two sets of contributions: (1) Under two types of congestion cost functions, we prove the existence of the primal generalized Nash equilibrium. The results are provided without a compactness assumption on the constraint set and are shown to hold when the mappings associated with the resulting variational inequality are non-monotone. Under further assumptions, the local and global uniqueness of the primal and primal-dual generalized Nash equilibrium is also provided. (2) We provide two distributed schemes for obtaining such equilibria: a dual and a primal-dual algorithm. Convergence of both algorithms is analyzed and preliminary numerical evidence is presented with the aid of an example.

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
Pages4649-4654
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

Fingerprint

Equilibrium Problem
Congestion
Nash Equilibrium
Costs
Congestion Games
Convergence of Algorithms
Primal-dual Algorithm
Solution Concepts
Primal-dual
Cost functions
Variational Inequalities
Compactness
Cost Function
Uniqueness

All Science Journal Classification (ASJC) codes

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

Cite this

Yin, H., Shanbhag, V. V., & Mehta, P. G. (2009). Nash equilibrium problems with congestion costs and shared constraints. In Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 (pp. 4649-4654). [5400502] (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2009.5400502
Yin, Huibing ; Shanbhag, Vinayak V. ; Mehta, Prashant G. / Nash equilibrium problems with congestion costs and shared constraints. Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009. 2009. pp. 4649-4654 (Proceedings of the IEEE Conference on Decision and Control).
@inproceedings{f0e912a8fc9546f49e0848603ae649f4,
title = "Nash equilibrium problems with congestion costs and shared constraints",
abstract = "Generalized Nash equilibria (GNE) represent extensions of the Nash solution concept when agents have shared strategy sets. This generalization is particularly relevant when agents compete in a networked setting. In this paper, we consider such a setting and focus on a congestion game in which agents contend with shared network constraints. We make two sets of contributions: (1) Under two types of congestion cost functions, we prove the existence of the primal generalized Nash equilibrium. The results are provided without a compactness assumption on the constraint set and are shown to hold when the mappings associated with the resulting variational inequality are non-monotone. Under further assumptions, the local and global uniqueness of the primal and primal-dual generalized Nash equilibrium is also provided. (2) We provide two distributed schemes for obtaining such equilibria: a dual and a primal-dual algorithm. Convergence of both algorithms is analyzed and preliminary numerical evidence is presented with the aid of an example.",
author = "Huibing Yin and Shanbhag, {Vinayak V.} and Mehta, {Prashant G.}",
year = "2009",
month = "12",
day = "1",
doi = "10.1109/CDC.2009.5400502",
language = "English (US)",
isbn = "9781424438716",
series = "Proceedings of the IEEE Conference on Decision and Control",
pages = "4649--4654",
booktitle = "Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009",

}

Yin, H, Shanbhag, VV & Mehta, PG 2009, Nash equilibrium problems with congestion costs and shared constraints. in Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009., 5400502, Proceedings of the IEEE Conference on Decision and Control, pp. 4649-4654, 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009, Shanghai, China, 12/15/09. https://doi.org/10.1109/CDC.2009.5400502

Nash equilibrium problems with congestion costs and shared constraints. / Yin, Huibing; Shanbhag, Vinayak V.; Mehta, Prashant G.

Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009. 2009. p. 4649-4654 5400502 (Proceedings of the IEEE Conference on Decision and Control).

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

TY - GEN

T1 - Nash equilibrium problems with congestion costs and shared constraints

AU - Yin, Huibing

AU - Shanbhag, Vinayak V.

AU - Mehta, Prashant G.

PY - 2009/12/1

Y1 - 2009/12/1

N2 - Generalized Nash equilibria (GNE) represent extensions of the Nash solution concept when agents have shared strategy sets. This generalization is particularly relevant when agents compete in a networked setting. In this paper, we consider such a setting and focus on a congestion game in which agents contend with shared network constraints. We make two sets of contributions: (1) Under two types of congestion cost functions, we prove the existence of the primal generalized Nash equilibrium. The results are provided without a compactness assumption on the constraint set and are shown to hold when the mappings associated with the resulting variational inequality are non-monotone. Under further assumptions, the local and global uniqueness of the primal and primal-dual generalized Nash equilibrium is also provided. (2) We provide two distributed schemes for obtaining such equilibria: a dual and a primal-dual algorithm. Convergence of both algorithms is analyzed and preliminary numerical evidence is presented with the aid of an example.

AB - Generalized Nash equilibria (GNE) represent extensions of the Nash solution concept when agents have shared strategy sets. This generalization is particularly relevant when agents compete in a networked setting. In this paper, we consider such a setting and focus on a congestion game in which agents contend with shared network constraints. We make two sets of contributions: (1) Under two types of congestion cost functions, we prove the existence of the primal generalized Nash equilibrium. The results are provided without a compactness assumption on the constraint set and are shown to hold when the mappings associated with the resulting variational inequality are non-monotone. Under further assumptions, the local and global uniqueness of the primal and primal-dual generalized Nash equilibrium is also provided. (2) We provide two distributed schemes for obtaining such equilibria: a dual and a primal-dual algorithm. Convergence of both algorithms is analyzed and preliminary numerical evidence is presented with the aid of an example.

UR - http://www.scopus.com/inward/record.url?scp=77950811663&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77950811663&partnerID=8YFLogxK

U2 - 10.1109/CDC.2009.5400502

DO - 10.1109/CDC.2009.5400502

M3 - Conference contribution

AN - SCOPUS:77950811663

SN - 9781424438716

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 4649

EP - 4654

BT - Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009

ER -

Yin H, Shanbhag VV, Mehta PG. Nash equilibrium problems with congestion costs and shared constraints. In Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009. 2009. p. 4649-4654. 5400502. (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2009.5400502