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Computing Normalized Equilibria in Convex-Concave Games

Author

Listed:
  • 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.

Suggested Citation

  • Flam, Sjur & Ruszczynski, A., 2006. "Computing Normalized Equilibria in Convex-Concave Games," Working Papers 2006:9, Lund University, Department of Economics.
  • Handle: RePEc:hhs:lunewp:2006_009
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    References listed on IDEAS

    as
    1. Steffan Berridge & Jacek Krawczyk, "undated". "Relaxation Algorithms in Finding Nash Equilibrium," Computing in Economics and Finance 1997 159, Society for Computational Economics.
    2. M.J. Kallio & A. Ruszczynski, 1994. "Perturbation Methods for Saddle Point Computation," Working Papers wp94038, International Institute for Applied Systems Analysis.
    3. A. Ruszczynski, 1994. "A Partial Regularization Method for Saddle Point Seeking," Working Papers wp94020, International Institute for Applied Systems Analysis.
    4. Flam, Sjur & Ruszczynski, A., 2006. "Computing Normalized Equilibria in Convex-Concave Games," Working Papers 2006:9, Lund University, Department of Economics.
    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. Flam, Sjur & Ruszczynski, A., 2006. "Computing Normalized Equilibria in Convex-Concave Games," Working Papers 2006:9, Lund University, Department of Economics.
    2. Sjur Didrik Flåm, 2016. "Noncooperative games, coupling constraints, and partial efficiency," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(2), pages 213-229, October.

    More about this item

    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;

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General

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