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Strategically robust implementation

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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.

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  • Ritesh Jain & Michele Lombardi & Antonio Penta, 2024. "Strategically robust implementation," Economics Working Papers 1893, Department of Economics and Business, Universitat Pompeu Fabra.
    • Handle: RePEc:upf:upfgen:1893
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    1. Mariann Ollár & Antonio Penta, 2017. "Full Implementation and Belief Restrictions," American Economic Review, American Economic Association, vol. 107(8), pages 2243-2277, August.
    2. 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..
    3. Marion Oury & Olivier Tercieux, 2012. "Continuous Implementation," PSE-Ecole d'économie de Paris (Postprint) halshs-00754580, HAL.
    4. 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..
    5. Mariann Ollar & Antonio Penta, 2023. "A network solution to robust implementation: the case of identical but unknown distributions," Post-Print hal-04198678, HAL.
    6. Mariann Ollár & Antonio Penta, 2023. "A Network Solution to Robust Implementation: The Case of Identical but Unknown Distributions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 90(5), pages 2517-2554.
    7. Dirk Bergemann & Stephen Morris, 2012. "Robust Mechanism Design," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 2, pages 49-96, World Scientific Publishing Co. Pte. Ltd..
    8. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(1), pages 23-38.
    9. Michele Lombardi & Ritesh Jain & Antonio Penta, 2024. "Strategically Robust Implementation," Working Papers 1461, Barcelona School of Economics.
    10. Kfir Eliaz, 2002. "Fault Tolerant Implementation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 69(3), pages 589-610.
    11. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-1028, July.
    12. Jackson, Matthew O, 1991. "Bayesian Implementation," Econometrica, Econometric Society, vol. 59(2), pages 461-477, March.
    13. 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.
    14. Tilman Börgers & Jiangtao Li, 2019. "Strategically Simple Mechanisms," Econometrica, Econometric Society, vol. 87(6), pages 2003-2035, November.
    15. Jain, Ritesh & Korpela, Ville & Lombardi, Michele, 2025. "Two-player rationalizable implementation," Journal of Economic Theory, Elsevier, vol. 227(C).
    16. Bergemann, Dirk & Morris, Stephen & Takahashi, Satoru, 2017. "Interdependent preferences and strategic distinguishability," Journal of Economic Theory, Elsevier, vol. 168(C), pages 329-371.
    17. 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..
    18. Arieli, Itai, 2010. "Rationalizability in continuous games," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 912-924, September.
    19. Penta, Antonio, 2015. "Robust dynamic implementation," Journal of Economic Theory, Elsevier, vol. 160(C), pages 280-316.
    20. 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.
    21. Marion Oury & Olivier Tercieux, 2012. "Continuous Implementation," Econometrica, Econometric Society, vol. 80(4), pages 1605-1637, July.
    22. , C. & ,, 2006. "Hierarchies of belief and interim rationalizability," Theoretical Economics, Econometric Society, vol. 1(1), pages 19-65, March.
    23. Dirk Bergemann & Stephen Morris, 2012. "Robust Mechanism Design:The Role of Private Information and Higher Order Beliefs," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 8318, April.
    24. Antonio Penta, 2012. "Higher Order Uncertainty and Information: Static and Dynamic Games," Econometrica, Econometric Society, vol. 80(2), pages 631-660, March.
    25. 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.
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    29. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, March.
    30. Abreu, Dilip & Matsushima, Hitoshi, 1992. "Virtual Implementation in Iteratively Undominated Strategies: Complete Information," Econometrica, Econometric Society, vol. 60(5), pages 993-1008, September.
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    More about this item

    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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