IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v175y2010i1p177-21110.1007-s10479-009-0653-x.html
   My bibliography  Save this article

Generalized Nash Equilibrium Problems

Author

Listed:
  • Francisco Facchinei
  • Christian Kanzow

Abstract

The Generalized Nash Equilibrium Problem is an important model that has its roots in the economic sciences but is being fruitfully used in many different fields. In this survey paper we aim at discussing its main properties and solution algorithms, pointing out what could be useful topics for future research in the field. Copyright Springer Science+Business Media, LLC 2010

Suggested Citation

  • Francisco Facchinei & Christian Kanzow, 2010. "Generalized Nash Equilibrium Problems," Annals of Operations Research, Springer, vol. 175(1), pages 177-211, March.
    • Handle: RePEc:spr:annopr:v:175:y:2010:i:1:p:177-211:10.1007/s10479-009-0653-x
    DOI: 10.1007/s10479-009-0653-x
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-009-0653-x
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-009-0653-x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. M. Margiocco & F. Patrone & L. Pusillo Chicco, 1999. "Metric Characterizations of Tikhonov Well-Posedness in Value," Journal of Optimization Theory and Applications, Springer, vol. 100(2), pages 377-387, February.
    2. Zhou, Jing & Lam, William H.K. & Heydecker, Benjamin G., 2005. "The generalized Nash equilibrium model for oligopolistic transit market with elastic demand," Transportation Research Part B: Methodological, Elsevier, vol. 39(6), pages 519-544, July.
    3. A. Heusinger & C. Kanzow, 2009. "Relaxation Methods for Generalized Nash Equilibrium Problems with Inexact Line Search," Journal of Optimization Theory and Applications, Springer, vol. 143(1), pages 159-183, October.
    4. Todd S. Munson & Francisco Facchinei & Michael C. Ferris & Andreas Fischer & Christian Kanzow, 2001. "The Semismooth Algorithm for Large Scale Complementarity Problems," INFORMS Journal on Computing, INFORMS, vol. 13(4), pages 294-311, November.
    5. Steven Gabriel & Yves Smeers, 2006. "Complementarity Problems in Restructured Natural Gas Markets," Lecture Notes in Economics and Mathematical Systems, in: Alberto Seeger (ed.), Recent Advances in Optimization, pages 343-373, Springer.
    6. Benjamin F. Hobbs & J. S. Pang, 2007. "Nash-Cournot Equilibria in Electric Power Markets with Piecewise Linear Demand Functions and Joint Constraints," Operations Research, INFORMS, vol. 55(1), pages 113-127, February.
    7. Steffan Berridge & Jacek Krawczyk, "undated". "Relaxation Algorithms in Finding Nash Equilibrium," Computing in Economics and Finance 1997 159, Society for Computational Economics.
    8. Michael R. Baye & Guoqiang Tian & Jianxin Zhou, 1993. "Characterizations of the Existence of Equilibria in Games with Discontinuous and Non-quasiconcave Payoffs," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(4), pages 935-948.
    9. Stephen M. Robinson, 1993. "Shadow Prices for Measures of Effectiveness, II: General Model," Operations Research, INFORMS, vol. 41(3), pages 536-548, June.
    10. D. Chan & J. S. Pang, 1982. "The Generalized Quasi-Variational Inequality Problem," Mathematics of Operations Research, INFORMS, vol. 7(2), pages 211-222, May.
    11. Nishimura, Kazuo & Friedman, James, 1981. "Existence of Nash Equilibrium in n Person Games without Quasi-Concavity," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 22(3), pages 637-648, October.
    12. Jacek Krawczyk, 2007. "Numerical solutions to coupled-constraint (or generalised Nash) equilibrium problems," Computational Management Science, Springer, vol. 4(2), pages 183-204, April.
    13. Anna Heusinger & Christian Kanzow, 2009. "Optimization reformulations of the generalized Nash equilibrium problem using Nikaido-Isoda-type functions," Computational Optimization and Applications, Springer, vol. 43(3), pages 353-377, July.
    14. Alejandro Jofré & Roger Wets, 2002. "Continuity Properties of Walras Equilibrium Points," Annals of Operations Research, Springer, vol. 114(1), pages 229-243, August.
    15. Debreu, Gerard, 1970. "Economies with a Finite Set of Equilibria," Econometrica, Econometric Society, vol. 38(3), pages 387-392, May.
    16. WEI, Jing-Yuan & SMEERS, Yves, 1999. "Spatial oligopolistic electricity models with Cournot generators and regulated transmission prices," LIDAM Reprints CORE 1454, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    17. Sun, Lian-Ju & Gao, Zi-You, 2007. "An equilibrium model for urban transit assignment based on game theory," European Journal of Operational Research, Elsevier, vol. 181(1), pages 305-314, August.
    18. Tian, Guoqiang & Zhou, Jianxin, 1995. "Transfer continuities, generalizations of the Weierstrass and maximum theorems: A full characterization," Journal of Mathematical Economics, Elsevier, vol. 24(3), pages 281-303.
    19. Eitan Altman & Odile Pourtallier & Alain Haurie & Francesco Moresino, 2000. "Approximating Nash Equilibria In Nonzero-Sum Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 2(02n03), pages 155-172.
    20. Partha Dasgupta & Eric Maskin, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, I: Theory," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(1), pages 1-26.
    21. Steven A. Gabriel & Supat Kiet & Jifang Zhuang, 2005. "A Mixed Complementarity-Based Equilibrium Model of Natural Gas Markets," Operations Research, INFORMS, vol. 53(5), pages 799-818, October.
    22. Xinmin Hu & Daniel Ralph & University of Cambridge, 2006. "Using EPECs to Model Bilevel Games in Restructured Electricity Markets with Locational Prices," Working Papers EPRG 0602, Energy Policy Research Group, Cambridge Judge Business School, University of Cambridge.
    23. Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, vol. 67(5), pages 1029-1056, September.
    24. Harker, Patrick T., 1991. "Generalized Nash games and quasi-variational inequalities," European Journal of Operational Research, Elsevier, vol. 54(1), pages 81-94, September.
    25. Partha Dasgupta & Eric Maskin, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, II: Applications," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(1), pages 27-41.
    26. Liqun Qi, 1993. "Convergence Analysis of Some Algorithms for Solving Nonsmooth Equations," Mathematics of Operations Research, INFORMS, vol. 18(1), pages 227-244, February.
    27. Jong-Shi Pang & Masao Fukushima, 2005. "Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games," Computational Management Science, Springer, vol. 2(1), pages 21-56, January.
    28. Wei Jing-Yuan & Yves Smeers, 1999. "Spatial Oligopolistic Electricity Models with Cournot Generators and Regulated Transmission Prices," Operations Research, INFORMS, vol. 47(1), pages 102-112, February.
    29. Stephen M. Robinson, 1993. "Shadow Prices for Measures of Effectiveness, I: Linear Model," Operations Research, INFORMS, vol. 41(3), pages 518-535, June.
    30. Harker, Patrick T. & Hong, Sungwook, 1994. "Pricing of track time in railroad operations: An internal market approach," Transportation Research Part B: Methodological, Elsevier, vol. 28(3), pages 197-212, June.
    31. Krawczyk, Jacek B., 2005. "Coupled constraint Nash equilibria in environmental games," Resource and Energy Economics, Elsevier, vol. 27(2), pages 157-181, June.
    32. M. Margiocco & F. Patrone & L. Pusillo, 2002. "On the Tikhonov Well-Posedness of Concave Games and Cournot Oligopoly Games," Journal of Optimization Theory and Applications, Springer, vol. 112(2), pages 361-379, February.
    33. Jacqueline Morgan & Vincenzo Scalzo, 2008. "Variational Stability Of Social Nash Equilibria," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 10(01), pages 17-24.
    34. E. Cavazzuti & M. Pappalardo & M. Passacantando, 2002. "Nash Equilibria, Variational Inequalities, and Dynamical Systems," Journal of Optimization Theory and Applications, Springer, vol. 114(3), pages 491-506, September.
    35. GABRIEL, Steven & SMEERS, Yves, 2006. "Complementarity problems in restructured natural gas markets," LIDAM Reprints CORE 1804, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    36. Hu, X. & Ralph, R., 2006. "Using EPECs to model bilevel games in restructured electricity markets with locational prices," Cambridge Working Papers in Economics 0619, Faculty of Economics, University of Cambridge.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Han, Deren & Zhang, Hongchao & Qian, Gang & Xu, Lingling, 2012. "An improved two-step method for solving generalized Nash equilibrium problems," European Journal of Operational Research, Elsevier, vol. 216(3), pages 613-623.
    2. Jiawang Nie & Xindong Tang & Lingling Xu, 2021. "The Gauss–Seidel method for generalized Nash equilibrium problems of polynomials," Computational Optimization and Applications, Springer, vol. 78(2), pages 529-557, March.
    3. Masao Fukushima, 2011. "Restricted generalized Nash equilibria and controlled penalty algorithm," Computational Management Science, Springer, vol. 8(3), pages 201-218, August.
    4. Rabia Nessah & Guoqiang Tian, 2016. "On the existence of Nash equilibrium in discontinuous games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(3), pages 515-540, March.
    5. J. Contreras & J. B. Krawczyk & J. Zuccollo, 2016. "Economics of collective monitoring: a study of environmentally constrained electricity generators," Computational Management Science, Springer, vol. 13(3), pages 349-369, July.
    6. Contreras, Javier & Krawczyk, Jacek & Zuccollo, James, 2008. "Can planners control competitive generators?," MPRA Paper 10395, University Library of Munich, Germany.
    7. Tian, Guoqiang, 2015. "On the existence of equilibria in games with arbitrary strategy spaces and preferences," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 9-16.
    8. Koichi Nabetani & Paul Tseng & Masao Fukushima, 2011. "Parametrized variational inequality approaches to generalized Nash equilibrium problems with shared constraints," Computational Optimization and Applications, Springer, vol. 48(3), pages 423-452, April.
    9. Rabia Nessah & Guoqiang Tian, 2008. "The Existence of Equilibria in Discontinuous and Nonconvex Games," Working Papers 2008-ECO-14, IESEG School of Management, revised Mar 2010.
    10. Rabia Nessah & Guoqiang Tian, 2013. "Existence of Solution of Minimax Inequalities, Equilibria in Games and Fixed Points Without Convexity and Compactness Assumptions," Journal of Optimization Theory and Applications, Springer, vol. 157(1), pages 75-95, April.
    11. Migot, Tangi & Cojocaru, Monica-G., 2020. "A parametrized variational inequality approach to track the solution set of a generalized nash equilibrium problem," European Journal of Operational Research, Elsevier, vol. 283(3), pages 1136-1147.
    12. Vincenzo Scalzo, 2013. "Essential equilibria of discontinuous games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(1), pages 27-44, September.
    13. Boucekkine, Raouf & Krawczyk, Jacek B. & Vallée, Thomas, 2010. "Towards an understanding of tradeoffs between regional wealth, tightness of a common environmental constraint and the sharing rules," Journal of Economic Dynamics and Control, Elsevier, vol. 34(9), pages 1813-1835, September.
    14. Francesco Ciardiello, 2007. "Convexity on Nash Equilibria without Linear Structure," Quaderni DSEMS 15-2007, Dipartimento di Scienze Economiche, Matematiche e Statistiche, Universita' di Foggia.
    15. Elnaz Kanani Kuchesfehani & Georges Zaccour, 2015. "S-adapted Equilibria in Games Played Over Event Trees with Coupled Constraints," Journal of Optimization Theory and Applications, Springer, vol. 166(2), pages 644-658, August.
    16. Axel Dreves & Christian Kanzow, 2011. "Nonsmooth optimization reformulations characterizing all solutions of jointly convex generalized Nash equilibrium problems," Computational Optimization and Applications, Springer, vol. 50(1), pages 23-48, September.
    17. Flam, Sjur & Ruszczynski, A., 2006. "Computing Normalized Equilibria in Convex-Concave Games," Working Papers 2006:9, Lund University, Department of Economics.
    18. Benjamin F. Hobbs & J. S. Pang, 2007. "Nash-Cournot Equilibria in Electric Power Markets with Piecewise Linear Demand Functions and Joint Constraints," Operations Research, INFORMS, vol. 55(1), pages 113-127, February.
    19. Jacek B. Krawczyk & Mabel Tidball, 2016. "Economic Problems with Constraints: How Efficiency Relates to Equilibrium," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 18(04), pages 1-19, December.
    20. F. Fakhar & H. R. Hajisharifi & Z. Soltani, 2023. "Noncoercive and noncontinuous equilibrium problems: existence theorem in infinite-dimensional spaces," Journal of Global Optimization, Springer, vol. 86(4), pages 989-1003, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:annopr:v:175:y:2010:i:1:p:177-211:10.1007/s10479-009-0653-x. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.