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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.

Suggested Citation

  • 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. Atsushi Kajii & Stephen Morris, 1997. "The Robustness of Equilibria to Incomplete Information," Econometrica, Econometric Society, vol. 65(6), pages 1283-1310, November.
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    2. Ronen Gradwohl & Rann Smorodinsky, 2021. "Privacy, Patience, and Protection," Dynamic Games and Applications, Springer, vol. 11(4), pages 759-784, December.
    3. Aramendia, Miguel & Wen, Quan, 2020. "Myopic perception in repeated games," Games and Economic Behavior, Elsevier, vol. 119(C), pages 1-14.
    4. 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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