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Cooperation in Repeated Games when the Number of Stages is Not Commonly Known


  • Abraham Neyman


An exponentially small departure from the common knowledge assumption on the number T of repetitions of the prisoners' dilemma already enables cooperation. More generally, with such a departure, any feasible individually rational outcome of any one-shot game can be approximated by an equilibrium of a finitely repeated version of that game. The departure from common knowledge is small in the following sense:(1) the players know T with precision +/-K; (2) with probability 1 - epsilon, the players know T precisely; moreover, this knowledge is mutual of order epsilon T; and (3) the deviation of T from its finite expectation is exponentially small.

Suggested Citation

  • Abraham Neyman, 1999. "Cooperation in Repeated Games when the Number of Stages is Not Commonly Known," Econometrica, Econometric Society, vol. 67(1), pages 45-64, January.
  • Handle: RePEc:ecm:emetrp:v:67:y:1999:i:1:p:45-64

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    References listed on IDEAS

    1. Currie, J. & Mcconnell, S., 1989. "Strikes And Arbitration In The Public Sector: Can Legislation Reduce Dispute Costs?," Papers 360, London School of Economics - Centre for Labour Economics.
    2. Max H. Bazerman & Henry S. Farber, 1985. "Arbitrator Decision Making: When are Final Offers Important?," ILR Review, Cornell University, ILR School, vol. 39(1), pages 76-89, October.
    3. Harrison, Glenn W, 1989. "Theory and Misbehavior of First-Price Auctions," American Economic Review, American Economic Association, vol. 79(4), pages 749-762, September.
    4. Bloom, David E & Cavanagh, Christopher L, 1986. "An Analysis of the Selection of Arbitrators," American Economic Review, American Economic Association, vol. 76(3), pages 408-422, June.
    5. Henry S. Farber & Harry C. Katz, 1979. "Interest Arbitration, Outcomes, and the Incentive to Bargain," ILR Review, Cornell University, ILR School, vol. 33(1), pages 55-63, October.
    6. Henry S. Farber & Max H. Bazerman, 1987. "Divergent Expectations as a Cause of Disagreement in Bargaining: Evidence from a Comparison of Arbitration Schemes."," NBER Working Papers 2139, National Bureau of Economic Research, Inc.
    7. Tracy, Joseph S, 1986. "An Investigation into the Determinants of U.S. Strike Activity," American Economic Review, American Economic Association, vol. 76(3), pages 423-436, June.
    8. Orley Ashenfelter & David Bloom, 1981. "Models of Arbitrator Behavior: Theory and Evidence," Working Papers 526, Princeton University, Department of Economics, Industrial Relations Section..
    9. Henry S. Farber & Max H. Bazerman, 1989. "Divergent Expectations as a Cause of Disagreement in Bargaining: Evidence from a Comparison of Arbitration Schemes," The Quarterly Journal of Economics, Oxford University Press, vol. 104(1), pages 99-120.
    10. Kalyan Chatterjee & William Samuelson, 1983. "Bargaining under Incomplete Information," Operations Research, INFORMS, vol. 31(5), pages 835-851, October.
    11. McConnell, Sheena, 1989. "Strikes, Wages, and Private Information," American Economic Review, American Economic Association, vol. 79(4), pages 801-815, September.
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    Cited by:

    1. Francois Cochard & Anthony Ziegelmeyer & Kene Boun My, 2005. "The Regulation of Nonpoint Emissions in the Laboratory: A Stress Test of the Ambient Tax Mechanism," Papers on Strategic Interaction 2005-37, Max Planck Institute of Economics, Strategic Interaction Group.
    2. Francesca Barigozzi & Renaud Bourlès & Dominique Henriet & Giuseppe Pignataro, 2017. "Pool size and the sustainability of optimal risk-sharing agreements," Theory and Decision, Springer, vol. 82(2), pages 273-303, February.
    3. Gagen, Michael, 2013. "Isomorphic Strategy Spaces in Game Theory," MPRA Paper 46176, University Library of Munich, Germany.
    4. Lisa Bruttel & Werner Güth & Ulrich Kamecke, 2012. "Finitely repeated prisoners’ dilemma experiments without a commonly known end," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(1), pages 23-47, February.
    5. Ambrus, Attila & Pathak, Parag A., 2011. "Cooperation over finite horizons: A theory and experiments," Journal of Public Economics, Elsevier, vol. 95(7), pages 500-512.
    6. Reichhuber, Anke & Camacho, Eva & Requate, Till, 2009. "A framed field experiment on collective enforcement mechanisms with Ethiopian farmers," Environment and Development Economics, Cambridge University Press, vol. 14(05), pages 641-663, October.
    7. repec:spr:jogath:v:46:y:2017:i:1:d:10.1007_s00182-015-0508-4 is not listed on IDEAS
    8. Abraham Neyman, 2012. "The value of two-person zero-sum repeated games with incomplete information and uncertain duration," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(1), pages 195-207, February.
    9. Conlon, John R., 2003. "Hope springs eternal: learning and the stability of cooperation in short horizon repeated games," Journal of Economic Theory, Elsevier, vol. 112(1), pages 35-65, September.
    10. Gilad Bavly, 2017. "Uncertainty in the traveler’s dilemma," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(1), pages 1-12, March.
    11. Renault, Regis, 2000. "Privately Observed Time Horizons in Repeated Games," Games and Economic Behavior, Elsevier, vol. 33(1), pages 117-125, October.
    12. repec:eee:gamebe:v:104:y:2017:i:c:p:92-130 is not listed on IDEAS
    13. Binenbaum, Eran & Pardey, Philip G., 2005. "Collective Action in Plant Breeding," 2005 Annual meeting, July 24-27, Providence, RI 19530, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    14. Rose Lai & Ko Wang & Jing Yang, 2007. "Stickiness of Rental Rates and Developers’ Option Exercise Strategies," The Journal of Real Estate Finance and Economics, Springer, vol. 34(1), pages 159-188, January.
    15. Gaël GIRAUD & Sonia WEYERS, 2003. "Strategic Market Games with a Finite Horizon and Incomplete," Working Papers of BETA 2003-04, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    16. Monderer, Dov & Tennenholtz, Moshe, 1999. "Distributed Games," Games and Economic Behavior, Elsevier, vol. 28(1), pages 55-72, July.
    17. Seale, Darryl A. & Arend, Richard J. & Phelan, Steven, 2006. "Modeling alliance activity: Opportunity cost effects and manipulations in an iterated prisoner's dilemma with exit option," Organizational Behavior and Human Decision Processes, Elsevier, vol. 100(1), pages 60-75, May.
    18. Gilad Bavly, 2011. "Elasticity of Games," Discussion Paper Series dp592, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    19. Neyman, Abraham, 2017. "Continuous-time stochastic games," Games and Economic Behavior, Elsevier, vol. 104(C), pages 92-130.

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