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Relaxation Algorithms in Finding Nash Equilibrium


  • Steffan Berridge
  • Jacek Krawczyk

    (Victoria University of Wellington)


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.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Steffan Berridge & Jacek Krawczyk, "undated". "Relaxation Algorithms in Finding Nash Equilibrium," Computing in Economics and Finance 1997 159, Society for Computational Economics.
  • Handle: RePEc:sce:scecf7:159

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    References listed on IDEAS

    1. Borjas, George J. & Sueyoshi, Glenn T., 1994. "A two-stage estimator for probit models with structural group effects," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 165-182.
    2. Butler, J S & Moffitt, Robert, 1982. "A Computationally Efficient Quadrature Procedure for the One-Factor Multinomial Probit Model," Econometrica, Econometric Society, vol. 50(3), pages 761-764, May.
    3. Gary Chamberlain, 1980. "Analysis of Covariance with Qualitative Data," Review of Economic Studies, Oxford University Press, vol. 47(1), pages 225-238.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Flam, Sjur & Ruszczynski, A., 2006. "Computing Normalized Equilibria in Convex-Concave Games," Working Papers 2006:9, Lund University, Department of Economics.
    5. Contreras, Javier & Krawczyk, Jacek & Zuccollo, James, 2008. "Can planners control competitive generators?," MPRA Paper 10395, University Library of Munich, Germany.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Mourad Ali & Patrick Rio, 2009. "Deterrence vs. Efficiency To Regulate Nonpoint Source Pollution," Working Papers 09-22, LAMETA, Universtiy of Montpellier, revised Dec 2009.
    11. 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.
    12. 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.
    13. Nils Langenberg, 2012. "Interior point methods for equilibrium problems," Computational Optimization and Applications, Springer, vol. 53(2), pages 453-483, October.
    14. 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.
    15. Shah, Sudhir A., 2005. "Optimal management of durable pollution," Journal of Economic Dynamics and Control, Elsevier, vol. 29(6), pages 1121-1164, June.
    16. 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.
    17. Contreras, Javier & Krawczyk, Jacek & Zuccollo, James, 2008. "The invisible polluter: Can regulators save consumer surplus?," MPRA Paper 9890, University Library of Munich, Germany.
    18. 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.
    19. 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.

    More about this item

    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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