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Computing Equilibria in Discounted 2 × 2 Supergames

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  • Kimmo Berg
  • Mitri Kitti

Abstract

This article examines the subgame perfect pure strategy equilibrium paths and payoff sets of discounted supergames with perfect monitoring. The main contribution is to provide methods for computing and tools for analyzing the equilibrium paths and payoffs in repeated games. We introduce the concept of a first-action feasible path, which simplifies the computation of equilibria. These paths can be composed into a directed multigraph, which is a useful representation for the equilibrium paths. We examine how the payoffs, discount factors and the properties of the multigraph affect the possible payoffs, their Hausdorff dimension, and the complexity of the equilibrium paths. The computational methods are applied to the 12 symmetric strictly ordinal 2 × 2 games. We find that these games can be classified into three groups based on the complexity of the equilibrium paths. Copyright Springer Science+Business Media, LLC. 2013

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  • Kimmo Berg & Mitri Kitti, 2013. "Computing Equilibria in Discounted 2 × 2 Supergames," Computational Economics, Springer;Society for Computational Economics, vol. 41(1), pages 71-88, January.
    • Handle: RePEc:kap:compec:v:41:y:2013:i:1:p:71-88
    DOI: 10.1007/s10614-011-9308-5
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    References listed on IDEAS

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    Cited by:

    1. Kimmo Berg & Gijs Schoenmakers, 2017. "Construction of Subgame-Perfect Mixed-Strategy Equilibria in Repeated Games," Games, MDPI, vol. 8(4), pages 1-14, November.
    2. Mitri Kitti, 2013. "Subgame Perfect Equilibria in Discounted Stochastic Games," Discussion Papers 87, Aboa Centre for Economics.
    3. Kimmo Berg & Markus Kärki, 2018. "Critical Discount Factor Values in Discounted Supergames," Games, MDPI, vol. 9(3), pages 1-17, July.
    4. Kimmo Berg, 2017. "Extremal Pure Strategies and Monotonicity in Repeated Games," Computational Economics, Springer;Society for Computational Economics, vol. 49(3), pages 387-404, March.
    5. Kimmo Berg, 2016. "Elementary Subpaths in Discounted Stochastic Games," Dynamic Games and Applications, Springer, vol. 6(3), pages 304-323, September.
    6. Jörn Künsemöller & Nan Zhang & Kimmo Berg & João Soares, 2017. "A game-theoretic evaluation of an ISP business model in caching," Information Systems Frontiers, Springer, vol. 19(4), pages 803-818, August.
    7. Mitri Kitti, 2013. "Conditional Markov equilibria in discounted dynamic games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 78(1), pages 77-100, August.
    8. Kimmo Berg & Mitri Kitti, 2014. "Equilibrium Paths in Discounted Supergames," Discussion Papers 96, Aboa Centre for Economics.
    9. Jörn Künsemöller & Nan Zhang & Kimmo Berg & João Soares, 0. "A game-theoretic evaluation of an ISP business model in caching," Information Systems Frontiers, Springer, vol. 0, pages 1-16.
    10. Mitri Kitti, 2014. "Equilibrium Payoffs for Pure Strategies in Repeated Games," Discussion Papers 98, Aboa Centre for Economics.

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