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Computing Normalized Equilibria in Convex-Concave Games

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Author Info

  • Flam, Sjur

    ()
    (Economics Department, Bergen University)

  • Ruszczynski, A.

    ()
    (Rutgers University, Department of Management Science and Information Systems)

Abstract

This paper considers a fairly large class of noncooperative games in which strategies are jointly constrained. When what is called the Ky Fan or Nikaido-Isoda function is convex-concave, selected Nash equilibria correspond to diagonal saddle points of that function. This feature is exploited to design computational algorithms for finding such equilibria. To comply with some freedom of individual choice the algorithms developed here are fairly decentralized. However, since coupling constraints must be enforced, repeated coordination is needed while underway towards equilibrium. Particular instances include zero-sum, two-person games - or minimax problems - that are convex-concave and involve convex coupling constraints.

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Bibliographic Info

Paper provided by Lund University, Department of Economics in its series Working Papers with number 2006:9.

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Length: 15 pages
Date of creation: 27 Apr 2006
Date of revision:
Handle: RePEc:hhs:lunewp:2006_009

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Postal: Department of Economics, School of Economics and Management, Lund University, Box 7082, S-220 07 Lund,Sweden
Phone: +46 +46 222 0000
Fax: +46 +46 2224613
Web page: http://www.nek.lu.se/en
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Related research

Keywords: Noncooperative games; Nash equilibrium; joint constraints; quasivariational inequalities; exact penalty; subgradient projection; proximal point algorithm; partial regularization; saddle points; Ky Fan or Nikaido-Isoda functions;

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  1. 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.
  2. A. Ruszczynski, 1994. "A Partial Regularization Method for Saddle Point Seeking," Working Papers wp94020, International Institute for Applied Systems Analysis.
  3. Jacek B. Krawczyk & Steffan Berridge, 1997. "Relaxation Algorithms in Finding Nash Equilibria," Computational Economics 9707002, EconWPA.
  4. M.J. Kallio & A. Ruszczynski, 1994. "Perturbation Methods for Saddle Point Computation," Working Papers wp94038, International Institute for Applied Systems Analysis.
  5. Krawczyk, Jacek B., 2005. "Coupled constraint Nash equilibria in environmental games," Resource and Energy Economics, Elsevier, vol. 27(2), pages 157-181, June.
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Cited by:
  1. 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.

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