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Repeated games with public deterministic monitoring

Listed author(s):
  • Laclau, Marie
  • Tomala, Tristan

We consider repeated games with compact actions sets and pure strategies in which players commonly observe a public signal which reveals imperfectly the action profile. We characterize the set of payoffs profiles that can be sustained by a perfect equilibrium, as players become increasingly patient. There are two conditions: admissibility and joint rationality. An admissibly feasible payoff can be achieved by an action profile that offers no unilateral deviation which is both undetectable and profitable. It is jointly rational if for all weights on players, the weighted average payoff is greater than or equal to the minmax level of the weighted average payoff function. This characterization is alternative to the one provided by the “score method” of Fudenberg and Levine (1994). We provide a simple construction of equilibrium strategies based on cooperation, punishments and rewards. Punishments rely on Blackwell's approachability algorithm.

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File URL: http://www.sciencedirect.com/science/article/pii/S0022053117300285
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Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 169 (2017)
Issue (Month): C ()
Pages: 400-424

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Handle: RePEc:eee:jetheo:v:169:y:2017:i:c:p:400-424
DOI: 10.1016/j.jet.2017.02.011
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622869

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  1. Tristan Tomala, 1998. "Pure equilibria of repeated games with public observation," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(1), pages 93-109.
  2. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476, January.
  3. Drew Fudenberg & David K. Levine & Satoru Takahashi, 2008. "Perfect public equilibrium when players are patient," World Scientific Book Chapters,in: A Long-Run Collaboration On Long-Run Games, chapter 16, pages 345-367 World Scientific Publishing Co. Pte. Ltd..
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  8. Fudenberg Drew & Levine David K., 1994. "Efficiency and Observability with Long-Run and Short-Run Players," Journal of Economic Theory, Elsevier, vol. 62(1), pages 103-135, February.
  9. Fudenberg, Drew & Levine, David I & Maskin, Eric, 1994. "The Folk Theorem with Imperfect Public Information," Econometrica, Econometric Society, vol. 62(5), pages 997-1039, September.
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  11. Fudenberg, Drew & Maskin, Eric, 1986. "The Folk Theorem in Repeated Games with Discounting or with Incomplete Information," Econometrica, Econometric Society, vol. 54(3), pages 533-554, May.
  12. Fudenberg, Drew & Maskin, Eric, 1991. "On the dispensability of public randomization in discounted repeated games," Journal of Economic Theory, Elsevier, vol. 53(2), pages 428-438, April.
  13. Renault, Jerome & Tomala, Tristan, 2004. "Communication equilibrium payoffs in repeated games with imperfect monitoring," Games and Economic Behavior, Elsevier, vol. 49(2), pages 313-344, November.
  14. Roy Radner & Roger Myerson & Eric Maskin, 1986. "An Example of a Repeated Partnership Game with Discounting and with Uniformly Inefficient Equilibria," Review of Economic Studies, Oxford University Press, vol. 53(1), pages 59-69.
  15. Sylvain Sorin, 1986. "On Repeated Games with Complete Information," Mathematics of Operations Research, INFORMS, vol. 11(1), pages 147-160, February.
  16. Wen, Quan, 1994. "The "Folk Theorem" for Repeated Games with Complete Information," Econometrica, Econometric Society, vol. 62(4), pages 949-954, July.
  17. Lehrer, E, 1990. "Nash Equilibria of n-Player Repeated Games with Semi-standard Information," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(2), pages 191-217.
  18. Abreu, Dilip & Pearce, David & Stacchetti, Ennio, 1990. "Toward a Theory of Discounted Repeated Games with Imperfect Monitoring," Econometrica, Econometric Society, vol. 58(5), pages 1041-1063, September.
  19. Neyman, Abraham, 2017. "Continuous-time stochastic games," Games and Economic Behavior, Elsevier, vol. 104(C), pages 92-130.
  20. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796.
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