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Safe Implementation in Mixed Nash Equilibrium

Author

Listed:
  • Anand Chopra
  • Malachy James Gavan
  • Antonio Penta

Abstract

Safe Implementation (Gavan and Penta, 2025) combines standard implementation with the requirement that the implementing mechanism is such that, if up to k agents deviate from the relevant solution concept, the outcomes that are induced are still 'acceptable' at every state of the world. In this paper, we study Safe Implementation of social choice correspondences in mixed Nash Equilibrium. We identify a condition, Set-Comonotonicity, which is both necessary and (under mild domain restrictions) almost sufficient for this implementation notion.

Suggested Citation

  • Anand Chopra & Malachy James Gavan & Antonio Penta, 2025. "Safe Implementation in Mixed Nash Equilibrium," Working Papers 1497, Barcelona School of Economics.
    • Handle: RePEc:bge:wpaper:1497
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    References listed on IDEAS

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    1. Mezzetti, Claudio & Renou, Ludovic, 2012. "Implementation in mixed Nash equilibrium," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2357-2375.
    2. Bochet, Olivier & Maniquet, François, 2010. "Virtual Nash implementation with admissible support," Journal of Mathematical Economics, Elsevier, vol. 46(1), pages 99-108, January.
    3. Ollar, Mariann & Penta, Antonio, 2024. "Incentive Compatibility and Belief Restrictions," TSE Working Papers 24-1558, Toulouse School of Economics (TSE).
    4. Healy, Paul J. & Peress, Michael, 2015. "Preference domains and the monotonicity of condorcet extensions," Economics Letters, Elsevier, vol. 130(C), pages 21-23.
    5. Mariann Ollár & Antonio Penta, 2017. "Full Implementation and Belief Restrictions," American Economic Review, American Economic Association, vol. 107(8), pages 2243-2277, August.
    6. Moore, John & Repullo, Rafael, 1990. "Nash Implementation: A Full Characterization," Econometrica, Econometric Society, vol. 58(5), pages 1083-1099, September.
    7. Benoît, Jean-Pierre & Ok, Efe A., 2008. "Nash implementation without no-veto power," Games and Economic Behavior, Elsevier, vol. 64(1), pages 51-67, September.
    8. Mariann Ollar & Antonio Penta, 2023. "A network solution to robust implementation: the case of identical but unknown distributions," Post-Print hal-04198678, HAL.
    9. Korpela, Ville, 2010. "Nash implementation theory -- A note on full characterizations," Economics Letters, Elsevier, vol. 108(3), pages 283-285, September.
    10. Olivier Bochet, 2007. "Nash Implementation with Lottery Mechanisms," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(1), pages 111-125, January.
    11. Siyang Xiong, 2022. "Nash implementation by stochastic mechanisms: a simple full characterization," Papers 2211.05431, arXiv.org.
    12. 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..
    13. 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.
    14. 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..
    15. Chopra, Anand & Gavan, Malachy James & Penta, Antonio, 2026. "Safe implementation in mixed Nash equilibrium," Journal of Mathematical Economics, Elsevier, vol. 122(C).
    16. Penta, Antonio, 2015. "Robust dynamic implementation," Journal of Economic Theory, Elsevier, vol. 160(C), pages 280-316.
    17. Dirk Bergemann & Stephen Morris, 2012. "Robust Virtual Implementation," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 8, pages 263-317, World Scientific Publishing Co. Pte. Ltd..
    18. Andrew Postlewaite & David Wettstein, 1989. "Feasible and Continuous Implementation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 56(4), pages 603-611.
    19. Müller, Christoph, 2016. "Robust virtual implementation under common strong belief in rationality," Journal of Economic Theory, Elsevier, vol. 162(C), pages 407-450.
    20. Hayashi, Takashi & Lombardi, Michele, 2019. "Constrained implementation," Journal of Economic Theory, Elsevier, vol. 183(C), pages 546-567.
    21. Gavan, Malachy J. & Penta, Antonio, 2025. "Safe implementation," Theoretical Economics, Econometric Society, vol. 20(4), November.
    22. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(1), pages 23-38.
    23. Ritesh Jain & Michele Lombardi & Antonio Penta, 2024. "Strategically robust implementation," Economics Working Papers 1893, Department of Economics and Business, Universitat Pompeu Fabra.
    24. Jackson, Matthew O. & Palfrey, Thomas R., 2003. "Corrigendum to "Voluntary implementation": J. Econ. Theor. 98 (2001) 1-25," Journal of Economic Theory, Elsevier, vol. 110(1), pages 204-205, May.
    25. Michele Lombardi & Ritesh Jain & Antonio Penta, 2024. "Strategically Robust Implementation," Working Papers 1461, Barcelona School of Economics.
    26. Kfir Eliaz, 2002. "Fault Tolerant Implementation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 69(3), pages 589-610.
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    Cited by:

    1. Chopra, Anand & Gavan, Malachy James & Penta, Antonio, 2026. "Safe implementation in mixed Nash equilibrium," Journal of Mathematical Economics, Elsevier, vol. 122(C).

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    Keywords

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    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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