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

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  • Abraham Neyman

Abstract

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.

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Bibliographic Info

Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 67 (1999)
Issue (Month): 1 (January)
Pages: 45-64

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Handle: RePEc:ecm:emetrp:v:67:y:1999:i:1:p:45-64

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Cited by:
  1. 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.
  2. Renault, R., 1997. "Privately Observed Time Horizons in Repeated Games," Papers 97.483, Toulouse - GREMAQ.
  3. Gilad Bavly, 2012. "Uncertainty in the Traveler's Dilemma," Discussion Paper Series dp595, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  4. 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.
  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. 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.
  7. 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).
  8. Abraham Neyman, 2012. "Continuous-time Stochastic Games," Discussion Paper Series dp616, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  9. Gagen, Michael, 2013. "Isomorphic Strategy Spaces in Game Theory," MPRA Paper 46176, University Library of Munich, Germany.
  10. Gilad Bavly, 2011. "Elasticity of Games," Discussion Paper Series dp592, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  11. Lisa Bruttel & Werner Güth & Ulrich Kamecke, 2012. "Finitely repeated prisoners’ dilemma experiments without a commonly known end," International Journal of Game Theory, Springer, vol. 41(1), pages 23-47, February.
  12. Reichhuber, Anke & Camacho Cuena, Eva & Requate, Till, 2008. "A Framed Field Experiment on Collective Enforcement Mechanisms with Ethiopian Farmers," Economics Working Papers 2008,11, Christian-Albrechts-University of Kiel, Department of Economics.
  13. Abraham Neyman, 2012. "The value of two-person zero-sum repeated games with incomplete information and uncertain duration," International Journal of Game Theory, Springer, vol. 41(1), pages 195-207, February.
  14. 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.
  15. Abraham Neyman, 2009. "The Value Of Two-Person Zero-Sum Repeated Games with Incomplete Information and Uncertain Duration," Discussion Paper Series dp512, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  16. 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.
  17. Monderer, Dov & Tennenholtz, Moshe, 1999. "Distributed Games," Games and Economic Behavior, Elsevier, vol. 28(1), pages 55-72, July.

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