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Instability of Belief-free Equilibria

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  • Yuval Heller

    () (Bar-Ilan University)

Abstract

Various papers have presented folk theorem results for repeated games with private monitoring that rely on belief-free equilibria. I show that these equilibria are not robust against small perturbations in the behavior of potential opponents. Specifically, I show that essentially none of the belief-free equilibria is evolutionarily stable, and that in generic games none of these equilibria is neutrally stable. Moreover, in a large family of games (which includes many public good games), the belief-free equilibria fail to satisfy even a very mild stability refinement.

Suggested Citation

  • Yuval Heller, 2017. "Instability of Belief-free Equilibria," Working Papers 2017-01, Bar-Ilan University, Department of Economics.
  • Handle: RePEc:biu:wpaper:2017-01
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    References listed on IDEAS

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    1. Yu Awaya & Vijay Krishna, 2016. "On Communication and Collusion," American Economic Review, American Economic Association, vol. 106(2), pages 285-315, February.
    2. Benaïm, Michel & Hofbauer, Josef & Hopkins, Ed, 2009. "Learning in games with unstable equilibria," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1694-1709, July.
    3. Mailath, George J. & Morris, Stephen, 2006. "Coordination failure in repeated games with almost-public monitoring," Theoretical Economics, Econometric Society, vol. 1(3), pages 311-340, September.
    4. Yamamoto, Yuichi, 2009. "A limit characterization of belief-free equilibrium payoffs in repeated games," Journal of Economic Theory, Elsevier, vol. 144(2), pages 802-824, March.
    5. Michihiro Kandori & Ichiro Obara, 2006. "Efficiency in Repeated Games Revisited: The Role of Private Strategies," Econometrica, Econometric Society, vol. 74(2), pages 499-519, March.
    6. Mailath, George J. & Morris, Stephen, 2002. "Repeated Games with Almost-Public Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 189-228, January.
    7. Hitoshi Matsushima, 2004. "Repeated Games with Private Monitoring: Two Players," Econometrica, Econometric Society, vol. 72(3), pages 823-852, May.
    8. repec:wsi:wschap:9789812818478_0012 is not listed on IDEAS
    9. Takahashi, Satoru, 2010. "Community enforcement when players observe partners' past play," Journal of Economic Theory, Elsevier, vol. 145(1), pages 42-62, January.
    10. Mailath, George J. & Olszewski, Wojciech, 2011. "Folk theorems with bounded recall under (almost) perfect monitoring," Games and Economic Behavior, Elsevier, vol. 71(1), pages 174-192, January.
    11. Michihiro Kandori, 2011. "Weakly Belief‐Free Equilibria in Repeated Games With Private Monitoring," Econometrica, Econometric Society, vol. 79(3), pages 877-892, May.
    12. Ely, Jeffrey C. & Valimaki, Juuso, 2002. "A Robust Folk Theorem for the Prisoner's Dilemma," Journal of Economic Theory, Elsevier, vol. 102(1), pages 84-105, January.
    13. Miyagawa, Eiichi & Miyahara, Yasuyuki & Sekiguchi, Tadashi, 2008. "The folk theorem for repeated games with observation costs," Journal of Economic Theory, Elsevier, vol. 139(1), pages 192-221, March.
    14. Bhaskar, V. & Obara, Ichiro, 2002. "Belief-Based Equilibria in the Repeated Prisoners' Dilemma with Private Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 40-69, January.
    15. van Veelen, Matthijs, 2012. "Robustness against indirect invasions," Games and Economic Behavior, Elsevier, vol. 74(1), pages 382-393.
    16. Olivier Compte, 1998. "Communication in Repeated Games with Imperfect Private Monitoring," Econometrica, Econometric Society, vol. 66(3), pages 597-626, May.
    17. Matsushima, Hitoshi, 1991. "On the theory of repeated games with private information : Part I: anti-folk theorem without communication," Economics Letters, Elsevier, vol. 35(3), pages 253-256, March.
    18. Drew Fudenberg & David Levine & Eric Maskin, 2008. "The Folk Theorem With Imperfect Public Information," World Scientific Book Chapters,in: A Long-Run Collaboration On Long-Run Games, chapter 12, pages 231-273 World Scientific Publishing Co. Pte. Ltd..
    19. Johannes Hörner & Wojciech Olszewski, 2009. "How Robust is the Folk Theorem?," The Quarterly Journal of Economics, Oxford University Press, vol. 124(4), pages 1773-1814.
    20. Yuichi Yamamoto, 2014. "Individual Learning and Cooperation in Noisy Repeated Games," Review of Economic Studies, Oxford University Press, vol. 81(1), pages 473-500.
    21. V. Bhaskar & George J. Mailath & Stephen Morris, 2008. "Purification in the Infinitely-Repeated Prisoners' Dilemma," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 11(3), pages 515-528, July.
    22. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, November.
    23. 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.
    24. Sekiguchi, Tadashi, 1997. "Efficiency in Repeated Prisoner's Dilemma with Private Monitoring," Journal of Economic Theory, Elsevier, vol. 76(2), pages 345-361, October.
    25. Hitoshi Matsushima & Tomomi Tanaka & Tomohisa Toyama, 2013. "Behavioral Approach to Repeated Games with Private Monitoring," CIRJE F-Series CIRJE-F-879, CIRJE, Faculty of Economics, University of Tokyo.
    26. Peski, Marcin, 2012. "An anti-folk theorem for finite past equilibria in repeated games with private monitoring," Theoretical Economics, Econometric Society, vol. 7(1), January.
    27. Kandori, Michihiro, 2002. "Introduction to Repeated Games with Private Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 1-15, January.
    28. Yamamoto, Yuichi, 2012. "Characterizing belief-free review-strategy equilibrium payoffs under conditional independence," Journal of Economic Theory, Elsevier, vol. 147(5), pages 1998-2027.
    29. Jeffrey C. Ely & Johannes Hörner & Wojciech Olszewski, 2005. "Belief-Free Equilibria in Repeated Games," Econometrica, Econometric Society, vol. 73(2), pages 377-415, March.
    30. Sugaya, Takuo & Takahashi, Satoru, 2013. "Coordination failure in repeated games with private monitoring," Journal of Economic Theory, Elsevier, vol. 148(5), pages 1891-1928.
    31. Obara, Ichiro, 2009. "Folk theorem with communication," Journal of Economic Theory, Elsevier, vol. 144(1), pages 120-134, January.
    32. Matsushima, Hitoshi, 1991. "On the theory of repeated games with private information : Part II: revelation through communication," Economics Letters, Elsevier, vol. 35(3), pages 257-261, March.
    33. Michihiro Kandori & Hitoshi Matsushima, 1998. "Private Observation, Communication and Collusion," Econometrica, Econometric Society, vol. 66(3), pages 627-652, May.
    34. Yamamoto, Yuichi, 2007. "Efficiency results in N player games with imperfect private monitoring," Journal of Economic Theory, Elsevier, vol. 135(1), pages 382-413, July.
    35. Yuichi Yamamoto, 2012. "Characterizing Belief-Free Review-Strategy Equilibrium Payoffs under ConditionalIndependence," PIER Working Paper Archive 12-005, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    36. Basu, Kaushik, 1994. "The Traveler's Dilemma: Paradoxes of Rationality in Game Theory," American Economic Review, American Economic Association, vol. 84(2), pages 391-395, May.
    37. Piccione, Michele, 2002. "The Repeated Prisoner's Dilemma with Imperfect Private Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 70-83, January.
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    More about this item

    Keywords

    Belief-free equilibrium; evolutionary stability; private monitoring; repeated Prisoner’s Dilemma; communication;

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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