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Relaxation Algorithms in Finding Nash Equilibria

Author

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  • Jacek B. Krawczyk

    (Victoria University of Wellington)

  • Steffan Berridge

    (Victoria University of Wellington)

Abstract

Relaxation algorithms provide a powerful method of finding noncooperative equilibria in general synchronous games. Through use of the Nikaido-Isoda function, the Nash solution to a broad category of constrained, multiplayer, non-zerosum games can easily be found. We provide solutions to some simple games using this procedure and extend ourselves to more difficult games involving coupled constraints and multiple discrete time periods using a program developed in Matlab.

Suggested Citation

  • Jacek B. Krawczyk & Steffan Berridge, 1997. "Relaxation Algorithms in Finding Nash Equilibria," Computational Economics 9707002, EconWPA.
  • Handle: RePEc:wpa:wuwpco:9707002
    Note: Type of Document - .zip (.tex .eps inside); prepared on UNIX LaTeX; to print on PostScript; pages: 28; figures: included .eps files. Presented at the 1997 Conference of the Society for Computational Economics, Stanford, California
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    Cited by:

    1. 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.
    2. Hiroyuki Kasahara & Katsumi Shimotsu, 2012. "Sequential Estimation of Structural Models With a Fixed Point Constraint," Econometrica, Econometric Society, vol. 80(5), pages 2303-2319, September.
    3. Flam, Sjur & Ruszczynski, A., 2006. "Computing Normalized Equilibria in Convex-Concave Games," Working Papers 2006:9, Lund University, Department of Economics.
    4. Krawczyk, Jacek & Zuccollo, James, 2006. "NIRA-3: An improved MATLAB package for finding Nash equilibria in infinite games," MPRA Paper 1119, University Library of Munich, Germany.
    5. Mourad Ali & Patrick Rio, 2009. "Deterrence vs. Efficiency To Regulate Nonpoint Source Pollution," Working Papers 09-22, LAMETA, Universitiy of Montpellier, revised Dec 2009.
    6. 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.
    7. Tran Quoc & Le Muu, 2012. "Iterative methods for solving monotone equilibrium problems via dual gap functions," Computational Optimization and Applications, Springer, vol. 51(2), pages 709-728, March.
    8. repec:spr:jglopt:v:70:y:2018:i:2:d:10.1007_s10898-017-0575-0 is not listed on IDEAS
    9. Shah, Sudhir A., 2005. "Optimal management of durable pollution," Journal of Economic Dynamics and Control, Elsevier, vol. 29(6), pages 1121-1164, June.
    10. repec:spr:decfin:v:40:y:2017:i:1:d:10.1007_s10203-017-0187-7 is not listed on IDEAS
    11. Francisco Facchinei & Jong-Shi Pang & Gesualdo Scutari, 2014. "Non-cooperative games with minmax objectives," Computational Optimization and Applications, Springer, vol. 59(1), pages 85-112, October.
    12. Contreras, Javier & Krawczyk, Jacek & Zuccollo, James, 2008. "Can planners control competitive generators?," MPRA Paper 10395, University Library of Munich, Germany.
    13. Watling, D.P. & Shepherd, S.P. & Koh, A., 2015. "Cordon toll competition in a network of two cities: Formulation and sensitivity to traveller route and demand responses," Transportation Research Part B: Methodological, Elsevier, vol. 76(C), pages 93-116.
    14. Lennox, Gareth D. & Gaston, Kevin J. & Acs, Szvetlana & Dallimer, Martin & Hanley, Nick & Armsworth, Paul R., 2013. "Conservation when landowners have bargaining power: Continuous conservation investments and cost uncertainty," Ecological Economics, Elsevier, vol. 93(C), pages 69-78.
    15. Krawczyk, Jacek & Azzato, Jeffrey, 2006. "NISOCSol an algorithm for approximating Markovian equilibria in dynamic games with coupled-constraints," MPRA Paper 1195, University Library of Munich, Germany.
    16. 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.
    17. Nils Langenberg, 2012. "Interior point methods for equilibrium problems," Computational Optimization and Applications, Springer, vol. 53(2), pages 453-483, October.
    18. Krawczyk, Jacek B & Townsend, Wilbur, 2014. "NIRA-GUI: A matlab application which solves for couple-constraint nash equibria from a symbolic specification," Working Paper Series 3414, Victoria University of Wellington, School of Economics and Finance.
    19. Gürkan, G. & Pang, J.S., 2009. "Approximizations of Nash equilibria," Other publications TiSEM de211d31-d77d-4211-9ca8-2, Tilburg University, School of Economics and Management.
    20. Contreras, Javier & Krawczyk, Jacek & Zuccollo, James, 2008. "The invisible polluter: Can regulators save consumer surplus?," MPRA Paper 9890, University Library of Munich, Germany.
    21. Bigi, Giancarlo & Castellani, Marco & Pappalardo, Massimo & Passacantando, Mauro, 2013. "Existence and solution methods for equilibria," European Journal of Operational Research, Elsevier, vol. 227(1), pages 1-11.
    22. 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.

    More about this item

    Keywords

    Computational economics; Nash normalised equilibrium; coupled constraints; Nikaido-Isoda function; open-loop Nash equilibrium;

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C87 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Econometric Software
    • E62 - Macroeconomics and Monetary Economics - - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook - - - Fiscal Policy
    • Q25 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation - - - Water

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