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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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    1. Atkeson, Andrew, 1991. "International Lending with Moral Hazard and Risk of Repudiation," Econometrica, Econometric Society, vol. 59(4), pages 1069-1089, July.
    2. Richard Ericson & Ariel Pakes, 1995. "Markov-Perfect Industry Dynamics: A Framework for Empirical Work," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 62(1), pages 53-82.
    3. Kenneth L. Judd & Sevin Yeltekin & James Conklin, 2003. "Computing Supergame Equilibria," Econometrica, Econometric Society, vol. 71(4), pages 1239-1254, July.
    4. Abreu, Dilip & Pearce, David & Stacchetti, Ennio, 1986. "Optimal cartel equilibria with imperfect monitoring," Journal of Economic Theory, Elsevier, vol. 39(1), pages 251-269, June.
    5. Ethan Ligon & Jonathan P. Thomas & Tim Worrall, 2000. "Mutual Insurance, Individual Savings and Limited Commitment," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 3(2), pages 216-246, April.
    6. Lars Ljungqvist & Thomas J. Sargent, 2004. "Recursive Macroeconomic Theory, 2nd Edition," MIT Press Books, The MIT Press, edition 2, volume 1, number 026212274x, April.
    7. Avinash Dixit & Gene M. Grossman & Faruk Gul, 2000. "The Dynamics of Political Compromise," Journal of Political Economy, University of Chicago Press, vol. 108(3), pages 531-568, June.
    8. Johannes Hörner & Takuo Sugaya & Satoru Takahashi & Nicolas Vieille, 2011. "Recursive Methods in Discounted Stochastic Games: An Algorithm for δ→ 1 and a Folk Theorem," Econometrica, Econometric Society, vol. 79(4), pages 1277-1318, July.
    9. Abreu, Dilip & Sannikov, Yuliy, 2014. "An algorithm for two-player repeated games with perfect monitoring," Theoretical Economics, Econometric Society, vol. 9(2), May.
    10. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796.
    11. Narayana R. Kocherlakota, 1996. "Implications of Efficient Risk Sharing without Commitment," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 63(4), pages 595-609.
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    4. Jose Miguel Abito & Cuicui Chen, 2021. "How much can we identify from repeated games?," Economics Bulletin, AccessEcon, vol. 41(3), pages 1212-1222.

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    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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