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A new necessary condition for implementation in iteratively undominated strategies

Author

Listed:
  • Takashi Kunimoto

    (McGill University and CIREQ)

  • Roberto Serrano

    (Brown University and IMDEA Social Sciences)

Abstract

Implementation in iteratively undominated strategies relies on permissive conditions. However, for the sufficiency results available, authors have relied on assumptions that amount to quasilinear preferences on a numeraire. We uncover a new necessary condition that implies that such assumptions cannot be dispensed with. We term the condition “restricted deception-proofness.” It requires that, in environments with identical preferences, the social choice function be immune to all deceptions, making it then stronger than incentive compatibility. In some environments the conditions for (exact or approximate) implementation are more restrictive than previously thought.

Suggested Citation

  • Takashi Kunimoto & Roberto Serrano, 2010. "A new necessary condition for implementation in iteratively undominated strategies," Working Papers 2010-03, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales.
    • Handle: RePEc:imd:wpaper:wp2010-03
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    Cited by:

    1. Jain, Ritesh, 2021. "Rationalizable implementation of social choice correspondences," Games and Economic Behavior, Elsevier, vol. 127(C), pages 47-66.
    2. Michele Crescenzi, 2025. "Nested Removal of Strictly Dominated Strategies in Infinite Games," Papers 2501.17685, arXiv.org, revised Jul 2025.
    3. Ritesh Jain & Michele Lombardi, 2019. "Virtual implementation by bounded mechanisms: Complete information," IEAS Working Paper : academic research 19-A001, Institute of Economics, Academia Sinica, Taipei, Taiwan.
    4. Artemov, Georgy, 2015. "Time and Nash implementation," Games and Economic Behavior, Elsevier, vol. 91(C), pages 229-236.
    5. Jain, Ritesh & Lombardi, Michele, 2022. "Continuous virtual implementation: Complete information," Journal of Mathematical Economics, Elsevier, vol. 99(C).
    6. Hsieh, Yue-Da & Qian, Xuewen & Qu, Chen, 2023. "Iterated bounded dominance," Economics Letters, Elsevier, vol. 232(C).
    7. Yi-Chun Chen & Xiao Luo & Chen Qu, 2016. "Rationalizability in general situations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(1), pages 147-167, January.
    8. Kunimoto, Takashi, 2020. "Robust virtual implementation with almost complete information," Mathematical Social Sciences, Elsevier, vol. 108(C), pages 62-73.
    9. Artemov, Georgy & Kunimoto, Takashi & Serrano, Roberto, 2013. "Robust virtual implementation: Toward a reinterpretation of the Wilson doctrine," Journal of Economic Theory, Elsevier, vol. 148(2), pages 424-447.

    More about this item

    Keywords

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    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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