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A branch-and-prune algorithm for discrete Nash equilibrium problems

Author

Listed:
  • Stefan Schwarze

    (Institute for Operations Research (IOR), Karlsruhe Institute of Technology (KIT))

  • Oliver Stein

    (Institute for Operations Research (IOR), Karlsruhe Institute of Technology (KIT))

Abstract

We present a branch-and-prune procedure for discrete Nash equilibrium problems with a convex description of each player’s strategy set. The derived pruning criterion does not require player convexity, but only strict convexity of some player’s objective function in a single variable. If satisfied, it prunes choices for this variable by stating activity of certain constraints. This results in a synchronous branching and pruning method. An algorithmic implementation and numerical tests are presented for randomly generated instances with convex polyhedral strategy sets and convex quadratic as well as non-convex quadratic objective functions.

Suggested Citation

  • Stefan Schwarze & Oliver Stein, 2023. "A branch-and-prune algorithm for discrete Nash equilibrium problems," Computational Optimization and Applications, Springer, vol. 86(2), pages 491-519, November.
    • Handle: RePEc:spr:coopap:v:86:y:2023:i:2:d:10.1007_s10589-023-00500-4
    DOI: 10.1007/s10589-023-00500-4
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    References listed on IDEAS

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    1. Axel Dreves & Christian Kanzow & Oliver Stein, 2012. "Nonsmooth optimization reformulations of player convex generalized Nash equilibrium problems," Journal of Global Optimization, Springer, vol. 53(4), pages 587-614, August.
    2. Carvalho, Margarida & Lodi, Andrea & Pedroso, João.P., 2022. "Computing equilibria for integer programming games," European Journal of Operational Research, Elsevier, vol. 303(3), pages 1057-1070.
    3. Francisco Facchinei & Veronica Piccialli & Marco Sciandrone, 2011. "Decomposition algorithms for generalized potential games," Computational Optimization and Applications, Springer, vol. 50(2), pages 237-262, October.
    4. Matthias Köppe & Christopher Thomas Ryan & Maurice Queyranne, 2011. "Rational Generating Functions and Integer Programming Games," Operations Research, INFORMS, vol. 59(6), pages 1445-1460, December.
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