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Robust dynamic implementation

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  • Penta, Antonio

Abstract

This paper extends the belief-free approach to robust mechanism design to dynamic environments, in which agents obtain information over time. A social choice function (SCF) is robustly partially implemented if it is perfect Bayesian incentive compatible for all possible beliefs. It is shown that this is possible if and only if the SCF is ex-post incentive compatible. Robust full implementation imposes the stronger condition that, for all possible beliefs, all Perfect Bayesian Equilibria induce outcomes consistent with the SCF. Characterizing the set of such equilibria is a key difficulty in studying this problem. This paper shows that, for a weaker notion of equilibrium, the set of all such equilibria can be computed by means of a recursive procedure which combines the logic of rationalizability and backward induction reasoning. These results are then used to show that, in environments with single-crossing preferences and well-behaved intertemporal effects, strict ex-post incentive compatibility and a condition which limits the strength of preference interdependencies are sufficient to guarantee robust full implementation.

Suggested Citation

  • Penta, Antonio, 2015. "Robust dynamic implementation," Journal of Economic Theory, Elsevier, vol. 160(C), pages 280-316.
  • Handle: RePEc:eee:jetheo:v:160:y:2015:i:c:p:280-316
    DOI: 10.1016/j.jet.2015.10.004
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    Cited by:

    1. Andrés Perea & Elias Tsakas, 2019. "Limited focus in dynamic games," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(2), pages 571-607, June.
    2. Guo, Huiyi & Yannelis, Nicholas C., 2022. "Robust coalitional implementation," Games and Economic Behavior, Elsevier, vol. 132(C), pages 553-575.
    3. Müller, Christoph, 2020. "Robust implementation in weakly perfect Bayesian strategies," Journal of Economic Theory, Elsevier, vol. 189(C).
    4. Battigalli, Pierpaolo & De Vito, Nicodemo, 2021. "Beliefs, plans, and perceived intentions in dynamic games," Journal of Economic Theory, Elsevier, vol. 195(C).
    5. Hitoshi Matsushima, 2021. "Partial ex-post verifiability and unique implementation of social choice functions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 56(3), pages 549-567, April.
    6. Hayashi, Takashi & Lombardi, Michele, 2019. "One-step-ahead implementation," Journal of Mathematical Economics, Elsevier, vol. 83(C), pages 110-126.
    7. Zuazo-Garin, Peio, 2017. "Uncertain information structures and backward induction," Journal of Mathematical Economics, Elsevier, vol. 71(C), pages 135-151.
    8. 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.
    9. Mackenzie, Andrew & Zhou, Yu, 2022. "Menu mechanisms," Journal of Economic Theory, Elsevier, vol. 204(C).
    10. Asheim, Geir B. & Brunnschweiler, Thomas, 2023. "Epistemic foundation of the backward induction paradox," Games and Economic Behavior, Elsevier, vol. 141(C), pages 503-514.
    11. Manili, Julien, 2024. "Order independence for rationalizability," Games and Economic Behavior, Elsevier, vol. 143(C), pages 152-160.
    12. Hitoshi Matsushima, 2019. "Partial Ex-Post Verifiability and Unique Implementation of Social Choice Functions (Forthcoming in Social Choice and Welfare)," CARF F-Series CARF-F-453, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    13. Guarino, Pierfrancesco, 2020. "An epistemic analysis of dynamic games with unawareness," Games and Economic Behavior, Elsevier, vol. 120(C), pages 257-288.
    14. Perea, Andrés, 2018. "Why forward induction leads to the backward induction outcome: A new proof for Battigalli's theorem," Games and Economic Behavior, Elsevier, vol. 110(C), pages 120-138.
    15. Hitoshi Matsushima, 2017. "Dynamic Implementation, Verification, and Detection," CARF F-Series CARF-F-416, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    16. Catonini, Emiliano, 2020. "On non-monotonic strategic reasoning," Games and Economic Behavior, Elsevier, vol. 120(C), pages 209-224.
    17. Perea, Andrés, 2017. "Forward induction reasoning and correct beliefs," Journal of Economic Theory, Elsevier, vol. 169(C), pages 489-516.
    18. Battigalli, P. & Catonini, E. & Manili, J., 2023. "Belief change, rationality, and strategic reasoning in sequential games," Games and Economic Behavior, Elsevier, vol. 142(C), pages 527-551.
    19. Andrés Perea & Arkadi Predtetchinski, 2019. "An epistemic approach to stochastic games," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(1), pages 181-203, March.
    20. Makris, Miltiadis & Renou, Ludovic, 2023. "Information design in multi-stage games," Theoretical Economics, Econometric Society, vol. 18(4), November.
    21. Müller, Christoph, 2016. "Robust virtual implementation under common strong belief in rationality," Journal of Economic Theory, Elsevier, vol. 162(C), pages 407-450.
    22. Safronov, Mikhail, 2018. "Coalition-proof full efficient implementation," Journal of Economic Theory, Elsevier, vol. 177(C), pages 659-677.

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    More about this item

    Keywords

    Backward induction reasoning; Dynamic mechanism design; Implementation; Rationalizability; Robustness;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • 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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