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Discounted Stochastic Games with Voluntary Transfers

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  • Sebastian Kranz

    (Dept. of Economics, University of Bonn, Institute for Energy Economics, University of Cologne)

Abstract

This paper studies discounted stochastic games perfect or imperfect public monitoring and the opportunity to conduct voluntary monetary transfers. We show that for all discount factors every public perfect equilibrium payoff can be implemented with a simple class of equilibria that have a stationary structure on the equilibrium path and optimal penal codes with a stick and carrot structure. We develop algorithms that exactly compute or approximate the set of equilibrium payoffs and find simple equilibria that implement these payoffs.

Suggested Citation

  • Sebastian Kranz, 2012. "Discounted Stochastic Games with Voluntary Transfers," Cowles Foundation Discussion Papers 1847, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1847
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    References listed on IDEAS

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    1. Goldlücke, Susanne & Kranz, Sebastian, 2013. "Renegotiation-proof relational contracts," Games and Economic Behavior, Elsevier, vol. 80(C), pages 157-178.
    2. Fudenberg, Drew & Yamamoto, Yuichi, 2011. "The folk theorem for irreducible stochastic games with imperfect public monitoring," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1664-1683, July.
    3. David Besanko & Ulrich Doraszelski, 2004. "Capacity Dynamics and Endogenous Asymmetries in Firm Size," RAND Journal of Economics, The RAND Corporation, vol. 35(1), pages 23-49, Spring.
    4. Fong, Yuk-fai & Surti, Jay, 2009. "The optimal degree of cooperation in the repeated Prisoners' Dilemma with side payments," Games and Economic Behavior, Elsevier, vol. 67(1), pages 277-291, September.
    5. Klimenko, Mikhail & Ramey, Garey & Watson, Joel, 2008. "Recurrent trade agreements and the value of external enforcement," Journal of International Economics, Elsevier, vol. 74(2), pages 475-499, March.
    6. Ariel Pakes & Paul McGuire, 1994. "Computing Markov-Perfect Nash Equilibria: Numerical Implications of a Dynamic Differentiated Product Model," RAND Journal of Economics, The RAND Corporation, vol. 25(4), pages 555-589, Winter.
    7. Katherine Doornik, 2006. "Relational Contracting in Partnerships," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 15(2), pages 517-548, June.
    8. 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.
    9. Jonathan Levin, 2003. "Relational Incentive Contracts," American Economic Review, American Economic Association, vol. 93(3), pages 835-857, June.
    10. Goldlücke, Susanne & Kranz, Sebastian, 2012. "Infinitely repeated games with public monitoring and monetary transfers," Journal of Economic Theory, Elsevier, vol. 147(3), pages 1191-1221.
    11. Luis Rayo, 2007. "Relational Incentives and Moral Hazard in Teams," Review of Economic Studies, Oxford University Press, vol. 74(3), pages 937-963.
    12. Andrew T. Ching, 2010. "A Dynamic Oligopoly Structural Model For The Prescription Drug Market After Patent Expiration," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 51(4), pages 1175-1207, November.
    13. MacLeod, W Bentley & Malcomson, James M, 1989. "Implicit Contracts, Incentive Compatibility, and Involuntary Unemployment," Econometrica, Econometric Society, vol. 57(2), pages 447-480, March.
    14. Joseph E. Harrington & Andrzej Skrzypacz, 2011. "Private Monitoring and Communication in Cartels: Explaining Recent Collusive Practices," American Economic Review, American Economic Association, vol. 101(6), pages 2425-2449, October.
    15. Markovich, Sarit & Moenius, Johannes, 2009. "Winning while losing: Competition dynamics in the presence of indirect network effects," International Journal of Industrial Organization, Elsevier, vol. 27(3), pages 346-357, May.
    16. Pakes, Ariel & McGuire, Paul, 2001. "Stochastic Algorithms, Symmetric Markov Perfect Equilibrium, and the 'Curse' of Dimensionality," Econometrica, Econometric Society, vol. 69(5), pages 1261-1281, September.
    17. David Besanko & Ulrich Doraszelski & Yaroslav Kryukov & Mark Satterthwaite, 2010. "Learning-by-Doing, Organizational Forgetting, and Industry Dynamics," Econometrica, Econometric Society, vol. 78(2), pages 453-508, March.
    18. Abreu, Dilip, 1988. "On the Theory of Infinitely Repeated Games with Discounting," Econometrica, Econometric Society, vol. 56(2), pages 383-396, March.
    19. Ulrich Doraszelski & Sarit Markovich, 2007. "Advertising dynamics and competitive advantage," RAND Journal of Economics, RAND Corporation, vol. 38(3), pages 557-592, September.
    20. Abreu, Dilip & Pearce, David & Stacchetti, Ennio, 1990. "Toward a Theory of Discounted Repeated Games with Imperfect Monitoring," Econometrica, Econometric Society, vol. 58(5), pages 1041-1063, September.
    21. Kenneth L. Judd & Sevin Yeltekin & James Conklin, 2003. "Computing Supergame Equilibria," Econometrica, Econometric Society, vol. 71(4), pages 1239-1254, July.
    22. Joseph E. Harrington Jr. & Andrzej Skrzypacz, 2007. "Collusion under monitoring of sales," RAND Journal of Economics, RAND Corporation, vol. 38(2), pages 314-331, June.
    23. Abreu, Dilip, 1986. "Extremal equilibria of oligopolistic supergames," Journal of Economic Theory, Elsevier, vol. 39(1), pages 191-225, June.
    24. Kranz, Sebastian & Ohlendorf, Susanne, 2009. "Renegotiation-Proof Relational Contracts with Side Payments," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 259, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
    25. C. Lanier Benkard, 2000. "Learning and Forgetting: The Dynamics of Aircraft Production," American Economic Review, American Economic Association, vol. 90(4), pages 1034-1054, September.
    26. 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.
    27. Jonathan Levin, 2002. "Multilateral Contracting and the Employment Relationship," The Quarterly Journal of Economics, Oxford University Press, vol. 117(3), pages 1075-1103.
    28. 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..
    29. Baliga, Sandeep & Evans, Robert, 2000. "Renegotiation in Repeated Games with Side-Payments," Games and Economic Behavior, Elsevier, vol. 33(2), pages 159-176, November.
    30. Yongyang Cai & Yongyang Cai & Kenneth L. Judd, 2017. "Computing Equilibria of Dynamic Games," Operations Research, INFORMS, vol. 65(2), pages 337-356, April.
    31. Abreu, Dilip & Sannikov, Yuliy, 2014. "An algorithm for two-player repeated games with perfect monitoring," Theoretical Economics, Econometric Society, vol. 9(2), May.
    32. Gautam Gowrisankaran & Robert J. Town, 1997. "Dynamic Equilibrium in the Hospital Industry," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 6(1), pages 45-74, March.
    33. Maskin, Eric & Tirole, Jean, 2001. "Markov Perfect Equilibrium: I. Observable Actions," Journal of Economic Theory, Elsevier, vol. 100(2), pages 191-219, October.
    34. David A. Miller & Joel Watson, 2013. "A Theory of Disagreement in Repeated Games With Bargaining," Econometrica, Econometric Society, vol. 81(6), pages 2303-2350, November.
    35. Christopher Sleet & Sevin Yeltekin, "undated". "On the Approximation of Value Correspondences," GSIA Working Papers 2007-E21, Carnegie Mellon University, Tepper School of Business.
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    Cited by:

    1. Sebastian Kranz, 2013. "Relational Contracting, Repeated Negotiations, and Hold-Up," Levine's Working Paper Archive 786969000000000676, David K. Levine.
    2. 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.

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    More about this item

    Keywords

    Stochastic games; Monetary transfers; Computation; Imperfect public monitoring; Public perfect equilibria;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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