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An algorithm for two-player repeated games with perfect monitoring


  • Abreu, Dilip

    () (Department of Economics, Princeton University)

  • Sannikov, Yuliy

    () (Department of Economics, Princeton University)


Consider repeated two-player games with perfect monitoring and discounting. We provide an algorithm that computes the set V* of payoff pairs of all pure-strategy subgame perfect equilibria with public randomization. The algorithm provides significant efficiency gains over the existing implementations of the algorithm from Abreu, Pearce and Stacchetti (1990). These efficiency gains arise from a better understanding of the manner in which extreme points of the equilibrium payoff set are generated. An important theoretical implication of our algorithm is that the set of extreme points E of V* is finite. Indeed, |E| ≤ 3|A|, where A is the set of action profiles of the stage game.

Suggested Citation

  • Abreu, Dilip & Sannikov, Yuliy, 2014. "An algorithm for two-player repeated games with perfect monitoring," Theoretical Economics, Econometric Society, vol. 9(2), May.
  • Handle: RePEc:the:publsh:1302

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    Cited by:

    1. Hörner, Johannes & Takahashi, Satoru & Vieille, Nicolas, 2014. "On the limit perfect public equilibrium payoff set in repeated and stochastic games," Games and Economic Behavior, Elsevier, vol. 85(C), pages 70-83.
    2. Azacis, Helmuts & Vida, Péter, 2015. "Repeated Implementation," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 518, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
    3. 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.
    4. Philipp Renner & Simon Scheidegger, 2017. "Machine learning for dynamic incentive problems," Working Papers 203620397, Lancaster University Management School, Economics Department.
    5. Dilip Abreu & Benjamin Brooks & Yuliy Sannikov, 2016. "A “Pencil Sharpening†Algorithm for Two Player Stochastic Games with Perfect Monitoring," Working Papers 78_2016, Princeton University, Department of Economics, Econometric Research Program..
    6. Kimmo Berg & Mitri Kitti, 2014. "Equilibrium Paths in Discounted Supergames," Discussion Papers 96, Aboa Centre for Economics.

    More about this item


    Repeated games; perfect monitoring; computation;

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games


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