International Journal of Game Theory

, Volume 44, Issue 2, pp 321–346 | Cite as

Cooperation under incomplete information on the discount factors

  • Cy Maor
  • Eilon SolanEmail author


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.


Repeated games Incomplete information Cooperation Common belief Rationalizability Prisoner’s dilemma 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Institute of MathematicsThe Hebrew UniversityJerusalemIsrael
  2. 2.The School of Mathematical SciencesTel Aviv UniversityTel AvivIsrael

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