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Repeated Relationships with Limits on Information Processing

  • Olivier Compte
  • Andrew Postlewaite

Many important strategic problems are characterized by repeated interactions among agents. There is a large literature in game theory and economics illustrating how considerations of future interactions can provide incentives for cooperation that would not be possible in one-shot interactions. Much of the work in repeated games assumes public monitoring: players observe precisely the same thing at each stage of the game. It is well-understood that even slight deviations from public monitoring increase dramatically the difficulty the problems players face in coordinating their actions. Repeated games with private monitoring incorporate differences in what players observe at each stage. Equilibria in repeated games with private monitoring, however, often seem unrealistic; the equilibrium strategies may be highly complex and very sensitive to the fine details of the stochastic relationship between players’ actions and observations. Furthermore, there is no realistic story about how players might arrive at their equilibrium strategies. We propose an alternative approach to understanding how people cooperate. Each player is endowed with a mental system that processes information: a mental system consists of a number of psychological states and a transition function between states that depends on observations made. In this world, a strategy is just a function from states to actions. Our framework has the following desirable properties: (i) players restrict attention to a relatively small set of simple strategies. (ii) the number of strategies that players compare is small enough that players might ultimately learn which perform well. We find that some mental systems allow agents to cooperate under a broad set of parameters, while others are not conducive to cooperation.

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Paper provided by David K. Levine in its series Levine's Working Paper Archive with number 122247000000002307.

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Date of creation: 03 Aug 2008
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Handle: RePEc:cla:levarc:122247000000002307
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  1. M. Kandori & G. Mailath & R. Rob, 1999. "Learning, Mutation and Long Run Equilibria in Games," Levine's Working Paper Archive 500, David K. Levine.
  2. Okuno-Fujiwara Masahiro & Postlewaite Andrew, 1995. "Social Norms and Random Matching Games," Games and Economic Behavior, Elsevier, vol. 9(1), pages 79-109, April.
  3. George J. Mailath & Stephen Morris, 1999. "Repeated Games with Almost-Public Monitoring," CARESS Working Papres almost-pub, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences, revised 01 Sep 2000.
  4. Olivier Compte, 1998. "Communication in Repeated Games with Imperfect Private Monitoring," Econometrica, Econometric Society, vol. 66(3), pages 597-626, May.
  5. repec:oup:restud:v:59:y:1992:i:1:p:63-80 is not listed on IDEAS
  6. Sainty, Barbara, 1999. "Achieving greater cooperation in a noisy prisoner's dilemma: an experimental investigation," Journal of Economic Behavior & Organization, Elsevier, vol. 39(4), pages 421-435, July.
  7. Piccione, Michele, 2002. "The Repeated Prisoner's Dilemma with Imperfect Private Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 70-83, January.
  8. Christopher Phelan & Andrzej Skrzypacz, 2007. "Private Monitoring with Infinite Histories," NajEcon Working Paper Reviews 843644000000000079,
  9. Michihiro Kandori & Hitoshi Matsushima, 1998. "Private Observation, Communication and Collusion," Econometrica, Econometric Society, vol. 66(3), pages 627-652, May.
  10. Michihiro Kandori & Ichiro Obara, 2007. "Finite State Equilibria in Dynamic Games," 2007 Meeting Papers 253, Society for Economic Dynamics.
  11. Miller, John H., 1996. "The coevolution of automata in the repeated Prisoner's Dilemma," Journal of Economic Behavior & Organization, Elsevier, vol. 29(1), pages 87-112, January.
  12. Jonathan Bendor & Roderick M. Kramer & Suzanne Stout, 1991. "When in Doubt..," Journal of Conflict Resolution, Peace Science Society (International), vol. 35(4), pages 691-719, December.
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