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Relaxation Algorithms in Finding Nash Equilibria

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Author Info

  • 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.

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Bibliographic Info

Paper provided by EconWPA in its series Computational Economics with number 9707002.

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Length: 28 pages
Date of creation: 19 Jul 1997
Date of revision:
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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Web page: http://128.118.178.162

Related research

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

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Cited by:
  1. Mourad Ali & Patrick Rio, 2009. "Deterrence vs. Efficiency To Regulate Nonpoint Source Pollution," Working Papers 09-22, LAMETA, Universtiy of Montpellier, revised Dec 2009.
  2. 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.
  3. 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.
  4. Kasahara, Hiroyuki & Shimotsu, Katsumi, 2009. "Sequential Estimation of Structural Models with a Fixed Point Constraint," Discussion Papers 2009-18, Graduate School of Economics, Hitotsubashi University.
  5. 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.
  6. Nils Langenberg, 2012. "Interior point methods for equilibrium problems," Computational Optimization and Applications, Springer, vol. 53(2), pages 453-483, October.
  7. Raouf Boucekkine & Jacek B. Krawczyk & Thomas Vallée, 2009. "Towards an understanding of tradeoffs between regional wealth, tightness of a common environmental constraint and the sharing rules," Working Papers hal-00422486, HAL.
  8. Contreras, Javier & Krawczyk, Jacek & Zuccollo, James, 2008. "The invisible polluter: Can regulators save consumer surplus?," MPRA Paper 9890, University Library of Munich, Germany.
  9. Flåm, Sjur Didrik & Ruszczynski, A., 2006. "Computing Normalized Equilibria in Convex-Concave Games," Working Papers in Economics 05/06, University of Bergen, Department of Economics.
  10. 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.
  11. 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.
  12. Contreras, Javier & Krawczyk, Jacek & Zuccollo, James, 2008. "Can planners control competitive generators?," MPRA Paper 10395, University Library of Munich, Germany.
  13. 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.
  14. Shah, Sudhir A., 2005. "Optimal management of durable pollution," Journal of Economic Dynamics and Control, Elsevier, vol. 29(6), pages 1121-1164, June.
  15. 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.

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