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Repeated proximity games

Author

Listed:
  • JÊrÆme Renault

    (CERMSEM, UniversitÊ Paris 1, PanthÊon-Sorbonne, 106-112 Bd de l'HÆpital, F-75647 Paris Cedex 13, France)

  • Tristan Tomala

    (CERMSEM, UniversitÊ Paris 1, PanthÊon-Sorbonne, 106-112 Bd de l'HÆpital, F-75647 Paris Cedex 13, France)

Abstract

We consider repeated games with complete information and imperfect monitoring, where each player is assigned a fixed subset of players and only observes the moves chosen by the players in this subset. This structure is naturally represented by a directed graph. We prove that a generalized folk theorem holds for any payoff function if and only if the graph is 2-connected, and then extend this result to the context of finitely repeated games.

Suggested Citation

  • JÊrÆme Renault & Tristan Tomala, 1998. "Repeated proximity games," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(4), pages 539-559.
    • Handle: RePEc:spr:jogath:v:27:y:1998:i:4:p:539-559
    Note: Received June 1997/Revised version March 1998
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    Citations

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    Cited by:

    1. Deb, Joyee & González-Díaz, Julio & Renault, Jérôme, 2016. "Uniform folk theorems in repeated anonymous random matching games," Games and Economic Behavior, Elsevier, vol. 100(C), pages 1-23.
    2. Laclau, M., 2014. "Communication in repeated network games with imperfect monitoring," Games and Economic Behavior, Elsevier, vol. 87(C), pages 136-160.
    3. Renault, Jérôme & Renou, Ludovic & Tomala, Tristan, 2014. "Secure message transmission on directed networks," Games and Economic Behavior, Elsevier, vol. 85(C), pages 1-18.
    4. Olivier Gossner & Tristan Tomala, 2007. "Secret Correlation in Repeated Games with Imperfect Monitoring," Mathematics of Operations Research, INFORMS, vol. 32(2), pages 413-424, May.
    5. Laclau, Marie, 2012. "A folk theorem for repeated games played on a network," Games and Economic Behavior, Elsevier, vol. 76(2), pages 711-737.
    6. Jérôme Renault & Tristan Tomala, 2011. "General Properties of Long-Run Supergames," Dynamic Games and Applications, Springer, vol. 1(2), pages 319-350, June.
    7. Tristan Tomala, 2011. "Fault Reporting in Partially Known Networks and Folk Theorems," Operations Research, INFORMS, vol. 59(3), pages 754-763, June.
    8. Nava, Francesco & Piccione, Michele, 2012. "Efficiency in repeated games with local interaction and uncertain local monitoring," LSE Research Online Documents on Economics 54250, London School of Economics and Political Science, LSE Library.
    9. Laclau, M., 2013. "Repeated games with local monitoring and private communication," Economics Letters, Elsevier, vol. 120(2), pages 332-337.
    10. Jérôme Renault, 2001. "Learning Sets in State Dependent Signalling Game Forms: A Characterization," Mathematics of Operations Research, INFORMS, vol. 26(4), pages 832-850, November.
    11. , & ,, 2014. "Efficiency in repeated games with local interaction and uncertain local monitoring," Theoretical Economics, Econometric Society, vol. 9(1), January.
    12. Polanski, Arnold, 2024. "Close-knit neighborhoods: Stability of cooperation in networks," Journal of Economic Theory, Elsevier, vol. 215(C).
    13. Yair Goldberg, 2003. "On the Minmax of Repeated Games with Imperfect Monitoring: A Computational Example," Discussion Paper Series dp345, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    14. Tomala, Tristan, 2009. "Perfect communication equilibria in repeated games with imperfect monitoring," Games and Economic Behavior, Elsevier, vol. 67(2), pages 682-694, November.
    15. Olivier Gossner & Rida Laraki & Tristan Tomala, 2004. "Maxmin computation and optimal correlation in repeated games with signals," Working Papers hal-00242940, HAL.
    16. Marie Laclau & Ludovic Renou & Xavier Venel, 2020. "Robust communication on networks," Papers 2007.00457, arXiv.org, revised Oct 2020.
    17. Markus Kinateder, 2006. "Repeated Games Played in a Network," UFAE and IAE Working Papers 674.06, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    18. 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.
    19. Olivier Gossner & Tristan Tomala, 2006. "Empirical Distributions of Beliefs Under Imperfect Observation," Mathematics of Operations Research, INFORMS, vol. 31(1), pages 13-30, February.
    20. Laclau, Marie & Renou, Ludovic & Venel, Xavier, 2024. "Communication on networks and strong reliability," Journal of Economic Theory, Elsevier, vol. 217(C).
    21. Fainmesser, Itay P. & Goldberg, David A., 2018. "Cooperation in partly observable networked markets," Games and Economic Behavior, Elsevier, vol. 107(C), pages 220-237.
    22. repec:dau:papers:123456789/6102 is not listed on IDEAS
    23. King, Maia, 2020. "The probabilities of node-to-node diffusion in fixed networks," SocArXiv dfq8y, Center for Open Science.
    24. Renault, Jerome & Tomala, Tristan, 2004. "Learning the state of nature in repeated games with incomplete information and signals," Games and Economic Behavior, Elsevier, vol. 47(1), pages 124-156, April.
    25. Marie Laclau & Ludovic Renou & Xavier Venel, 2024. "Communication on networks and strong reliability," Working Papers hal-03099678, HAL.

    More about this item

    Keywords

    Repeated games · Folk theorem · imperfect monitoring · graphs;

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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