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Relaxation Algorithms in Finding Nash Equilibrium

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  • Steffan Berridge
  • Jacek Krawczyk

    (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 Society for Computational Economics in its series Computing in Economics and Finance 1997 with number 159.

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Handle: RePEc:sce:scecf7:159

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Postal: CEF97, Stanford University, Department of Economics, Stanford CA USA
Web page: http://bucky.stanford.edu/cef97/
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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. 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. 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. Contreras, Javier & Krawczyk, Jacek & Zuccollo, James, 2008. "Can planners control competitive generators?," MPRA Paper 10395, University Library of Munich, Germany.
  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. 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. Contreras, Javier & Krawczyk, Jacek & Zuccollo, James, 2008. "The invisible polluter: Can regulators save consumer surplus?," MPRA Paper 9890, University Library of Munich, Germany.
  8. 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.
  9. Hiroyuki Kasahara & Katsumi Shimotsu, 2012. "Sequential Estimation of Structural Models With a Fixed Point Constraint," Econometrica, Econometric Society, vol. 80(5), pages 2303-2319, 09.
  10. 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.
  11. 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.
  12. Shah, Sudhir A., 2005. "Optimal management of durable pollution," Journal of Economic Dynamics and Control, Elsevier, vol. 29(6), pages 1121-1164, June.
  13. 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.
  14. Nils Langenberg, 2012. "Interior point methods for equilibrium problems," Computational Optimization and Applications, Springer, vol. 53(2), pages 453-483, October.
  15. 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.

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