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Strategically Robust Implementation

Author

Listed:
  • Ritesh Jain
  • Michele Lombardi
  • Antonio Penta

Abstract

We put forward a notion of implementation for Social Choice Functions (SCF) that is robust with respect to the solution concept used to model agents’ strategic interaction. Formally, we define implementation in Interim Correlated Rationalizability and its Refinements (ICRR implementation) as implementation in Interim Correlated Rationalizability (ICR), with the extra requirement that it be achieved by a mechanism in which all selections from ICR have the best-reply property. We provide a tight characterization in terms of a novel notion of monotonicity, Iterative Interim Monotonicity (IIM). Our condition relates the possibility of ICRR-implementation with a specific way in which the SCF is constrained by agents’ preference reversals. We provide several alternative formulations of IIM, that clarify both its connection with various parts of the literature (such as Oury and Tercieux (2012)’s Interim Rationalizable Monotonicity, and others), and the source of IIM’s ability to overcome several limitations of the previous conditions in the literature.

Suggested Citation

  • Ritesh Jain & Michele Lombardi & Antonio Penta, 2024. "Strategically Robust Implementation," Working Papers 1461, Barcelona School of Economics.
    • Handle: RePEc:bge:wpaper:1461
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    References listed on IDEAS

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    1. Dirk Bergemann & Stephen Morris, 2012. "Robust Implementation in General Mechanisms," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 5, pages 195-239, World Scientific Publishing Co. Pte. Ltd..
    2. Tilman Börgers & Jiangtao Li, 2019. "Strategically Simple Mechanisms," Econometrica, Econometric Society, vol. 87(6), pages 2003-2035, November.
    3. Mariann Ollár & Antonio Penta, 2017. "Full Implementation and Belief Restrictions," American Economic Review, American Economic Association, vol. 107(8), pages 2243-2277, August.
    4. Dirk Bergemann & Stephen Morris & Olivier Tercieux, 2012. "Rationalizable Implementation," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 11, pages 375-404, World Scientific Publishing Co. Pte. Ltd..
    5. Dirk Bergemann & Stephen Morris, 2012. "Robust Implementation in Direct Mechanisms," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 4, pages 153-194, World Scientific Publishing Co. Pte. Ltd..
    6. Ritesh Jain & Ville Korpela & Michele Lombardi, 2022. "Two-Player Rationalizable Implementation," CSEF Working Papers 660, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    7. Mariann Ollar & Antonio Penta, 2023. "A network solution to robust implementation: the case of identical but unknown distributions," Post-Print hal-04198678, HAL.
    8. Marion Oury & Olivier Tercieux, 2012. "Continuous Implementation," Econometrica, Econometric Society, vol. 80(4), pages 1605-1637, July.
    9. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    10. Bergemann, Dirk & Morris, Stephen & Takahashi, Satoru, 2017. "Interdependent preferences and strategic distinguishability," Journal of Economic Theory, Elsevier, vol. 168(C), pages 329-371.
    11. , C. & ,, 2006. "Hierarchies of belief and interim rationalizability," Theoretical Economics, Econometric Society, vol. 1(1), pages 19-65, March.
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    14. Antonio Penta, 2012. "Higher Order Uncertainty and Information: Static and Dynamic Games," Econometrica, Econometric Society, vol. 80(2), pages 631-660, March.
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    16. Battigalli Pierpaolo & Di Tillio Alfredo & Grillo Edoardo & Penta Antonio, 2011. "Interactive Epistemology and Solution Concepts for Games with Asymmetric Information," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 11(1), pages 1-40, March.
    17. Matthew O. Jackson, 1992. "Implementation in Undominated Strategies: A Look at Bounded Mechanisms," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 59(4), pages 757-775.
    18. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(1), pages 23-38.
    19. Kfir Eliaz, 2002. "Fault Tolerant Implementation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 69(3), pages 589-610.
    20. Arieli, Itai, 2010. "Rationalizability in continuous games," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 912-924, September.
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    22. Penta, Antonio, 2015. "Robust dynamic implementation," Journal of Economic Theory, Elsevier, vol. 160(C), pages 280-316.
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    24. Jain, Ritesh & Lombardi, Michele & Müller, Christoph, 2023. "An alternative equivalent formulation for robust implementation," Games and Economic Behavior, Elsevier, vol. 142(C), pages 368-380.
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    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    full implementation; Bayes Nash equilibrium; interim correlated rationalizability; robustness;
    All these keywords.

    JEL classification:

    • C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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