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Cooperation under Incomplete Information on the Discount Factors

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  • Cy Maor
  • Eilon Solan

Abstract

In repeated games, cooperation is possible in equilibrium only if players are sufficiently patient, and long-term gains from cooperation outweigh short-term gains from deviation. What happens if the players have incomplete information regarding each other's discount factors? In this paper we look at repeated games in which each player has incomplete information regarding the other player's discount factor, and ask when full cooperation can arise in equilibrium. We provide necessary and sufficient conditions that allow full cooperation in equilibrium that is composed of grim trigger strategies, and characterize the states of the world in which full cooperation occurs. We then ask whether these "cooperation events" are close to those in the complete information case, when the information on the other player's discount factor is "almost" complete.

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  • Cy Maor & Eilon Solan, 2014. "Cooperation under Incomplete Information on the Discount Factors," Papers 1411.1368, arXiv.org.
    • Handle: RePEc:arx:papers:1411.1368
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    1. Stephen Morris, 1999. "Approximate common knowledge revisited," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(3), pages 385-408.
    2. Jonathan Weinstein & Muhamet Yildiz, 2007. "A Structure Theorem for Rationalizability with Application to Robust Predictions of Refinements," Econometrica, Econometric Society, vol. 75(2), pages 365-400, March.
    3. Watson, Joel, 2002. "Starting Small and Commitment," Games and Economic Behavior, Elsevier, vol. 38(1), pages 176-199, January.
    4. Atsushi Kajii & Stephen Morris, 1997. "The Robustness of Equilibria to Incomplete Information," Econometrica, Econometric Society, vol. 65(6), pages 1283-1310, November.
    5. Ehud Lehrer & Leeat Yariv, 1999. "Repeated Games with Incomplete Information on One Side: The Case of Different Discount Factors," Mathematics of Operations Research, INFORMS, vol. 24(1), pages 204-218, February.
    6. Ezra Einy & Ori Haimanko & Diego Moreno & Benyamin Shitovitz, 2008. "Uniform Continuity of the Value of Zero-Sum Games with Differential Information," Mathematics of Operations Research, INFORMS, vol. 33(3), pages 552-560, August.
    7. Watson, Joel, 1999. "Starting Small and Renegotiation," Journal of Economic Theory, Elsevier, vol. 85(1), pages 52-90, March.
    8. , & ,, 2011. "Robustness to incomplete information in repeated games," Theoretical Economics, Econometric Society, vol. 6(1), January.
    9. Maschler,Michael & Solan,Eilon & Zamir,Shmuel, 2013. "Game Theory," Cambridge Books, Cambridge University Press, number 9781107005488.
    10. Kajii, Atsushi & Morris, Stephen, 1997. "Commonp-Belief: The General Case," Games and Economic Behavior, Elsevier, vol. 18(1), pages 73-82, January.
    11. Ehud Lehrer & Ady Pauzner, 1999. "Repeated Games with Differential Time Preferences," Econometrica, Econometric Society, vol. 67(2), pages 393-412, March.
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    Cited by:

    1. Aramendia, Miguel & Wen, Quan, 2020. "Myopic perception in repeated games," Games and Economic Behavior, Elsevier, vol. 119(C), pages 1-14.
    2. Ronen Gradwohl & Rann Smorodinsky, 2021. "Privacy, Patience, and Protection," Dynamic Games and Applications, Springer, vol. 11(4), pages 759-784, December.
    3. Zeng, Weijun & Ai, Hongfeng & Zhao, Man, 2019. "Asymmetrical expectations of future interaction and cooperation in the iterated prisoner's dilemma game," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 148-164.

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