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Robust Predictions in Infinite-Horizon Games--an Unrefinable Folk Theorem

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  • Jonathan Weinstein
  • Muhamet Yildiz

Abstract

We show that in any game that is continuous at infinity, if a plan of action a i is played by a type t i in a Bayesian Nash equilibrium, then there are perturbations of t i for which a i is the only rationalizable plan and whose unique rationalizable belief regarding the play of the game is arbitrarily close to the equilibrium belief of t i . As an application to repeated games, we prove an unrefinable folk theorem: any individually rational and feasible payoff is the unique rationalizable payoff vector for some perturbed type profile. This is true even if perturbed types are restricted to believe that the repeated-game payoff structure and the discount factor are common knowledge. Copyright , Oxford University Press.

Suggested Citation

  • Jonathan Weinstein & Muhamet Yildiz, 2013. "Robust Predictions in Infinite-Horizon Games--an Unrefinable Folk Theorem," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 80(1), pages 365-394.
    • Handle: RePEc:oup:restud:v:80:y:2013:i:1:p:365-394
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    File URL: http://hdl.handle.net/10.1093/restud/rds027
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    Cited by:

    1. Müller, Christoph, 2020. "Robust implementation in weakly perfect Bayesian strategies," Journal of Economic Theory, Elsevier, vol. 189(C).
    2. Takahashi, Satoru & Tercieux, Olivier, 2020. "Robust equilibrium outcomes in sequential games under almost common certainty of payoffs," Journal of Economic Theory, Elsevier, vol. 188(C).
    3. Shuo Liu & Harry Pei, 2017. "Monotone equilibria in signalling games," ECON - Working Papers 252, Department of Economics - University of Zurich.
    4. Antonio Penta & Peio Zuazo-Garin, 2022. "Rationalizability, Observability, and Common Knowledge [Player Importance and Forward Induction]," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 89(2), pages 948-975.
    5. Penta, Antonio, 2015. "Robust dynamic implementation," Journal of Economic Theory, Elsevier, vol. 160(C), pages 280-316.
    6. Heifetz, Aviad & Kets, Willemien, 2018. "Robust multiplicity with a grain of naiveté," Theoretical Economics, Econometric Society, vol. 13(1), January.
    7. Weinstein, Jonathan & Yildiz, Muhamet, 2017. "Interim correlated rationalizability in infinite games," Journal of Mathematical Economics, Elsevier, vol. 72(C), pages 82-87.
    8. Tsoy, Anton, 2018. "Alternating-offer bargaining with the global games information structure," Theoretical Economics, Econometric Society, vol. 13(2), May.

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