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A "Pencil-Sharpening" Algorithm for Two Player Stochastic Games with Perfect Monitoring

Author

Listed:
  • Abreu, Dilip

    (Princeton University)

  • Brooks, Benjamin

    (University of Chicago)

  • Sannikov, Yuliy

    (Princeton University)

Abstract

We study the subgame perfect equilibria of two player stochastic games with perfect monitoring and geometric discounting. A novel algorithm is developed for calculating the discounted payoffs that can be attained in equilibrium. This algorithm generates a sequence of tuples of payoffs vectors, one payoff for each state, that move around the equilibrium payoff sets in a clockwise manner. The trajectory of these "pivot" payoffs asymptotically traces the boundary of the equilibrium payoff correspondence. We also provide an implementation of our algorithm, and preliminary simulations indicate that it is more efficient than existing methods. The theoretical results that underlie the algorithm also yield a bound on the number of extremal equilibrium payoffs.

Suggested Citation

  • Abreu, Dilip & Brooks, Benjamin & Sannikov, Yuliy, 2016. "A "Pencil-Sharpening" Algorithm for Two Player Stochastic Games with Perfect Monitoring," Research Papers 3428, Stanford University, Graduate School of Business.
    • Handle: RePEc:ecl:stabus:3428
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    Cited by:

    1. Āzacis, Helmuts & Vida, Péter, 2019. "Repeated implementation: A practical characterization," Journal of Economic Theory, Elsevier, vol. 180(C), pages 336-367.
    2. Suehyun Kwon, 2019. "Dynamic IC and dynamic programming," CESifo Working Paper Series 7564, CESifo.
    3. Jose Miguel Abito & Cuicui Chen, 2021. "How much can we identify from repeated games?," Economics Bulletin, AccessEcon, vol. 41(3), pages 1212-1222.
    4. Susanne Goldlücke & Sebastian Kranz, 2018. "Discounted stochastic games with voluntary transfers," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(1), pages 235-263, July.

    More about this item

    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
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General

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