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Safe Implementation

Author

Listed:
  • Gavan, Malachy James
  • Penta, Antonio

Abstract

We introduce Safe Implementation, a notion of implementation that adds to the standard requirements the restriction that deviations from the baseline solution concept induce outcomes that are acceptable. The primitives of Safe Implementation therefore include both a Social Choice Correspondence, as standard, and an Acceptability Correspondence, each mapping every state of the world to a subset of allocations. This framework generalizes standard notions of implementation, and can accommodate a variety of considerations, including robustness concerns with respect to mistakes in play, model misspecification, behavioral considerations, state-dependent feasibility restrictions, limited commitment, etc. We provide results both for general solution concepts and for the case in which agents’ interaction is modelled by Nash Equilibrium. In the latter case, we identify necessary and sufficient conditions (namely, Comonotonicity and safety-no veto) that restrict the joint behavior of the Social Choice and Acceptability Correspondences. These conditions are more stringent than Maskin’s (1978), but coincide with them when the safety requirements are vacuous. We also show that these conditions are quite permissive in important economic applications, such as environments with single-crossing preferences and in problems of efficient allocation of in-divisible goods, but also that Safe Implementation can be very demanding in environments with ‘rich’ preferences, regardless of the underlying solution concept.

Suggested Citation

  • Gavan, Malachy James & Penta, Antonio, 2022. "Safe Implementation," TSE Working Papers 22-1369, Toulouse School of Economics (TSE).
  • Handle: RePEc:tse:wpaper:127416
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    References listed on IDEAS

    as
    1. Gneezy, Uri & Rustichini, Aldo, 2000. "A Fine is a Price," The Journal of Legal Studies, University of Chicago Press, vol. 29(1), pages 1-17, January.
    2. Mariann Ollár & Antonio Penta, 2017. "Full Implementation and Belief Restrictions," American Economic Review, American Economic Association, vol. 107(8), pages 2243-2277, August.
    3. 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..
    4. Dutta, Bhaskar & Sen, Arunava, 2012. "Nash implementation with partially honest individuals," Games and Economic Behavior, Elsevier, vol. 74(1), pages 154-169.
    5. Michele Lombardi & Naoki Yoshihara, 2020. "Partially-honest Nash implementation: a full characterization," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(3), pages 871-904, October.
    6. Renou, Ludovic & Schlag, Karl H., 2011. "Implementation in minimax regret equilibrium," Games and Economic Behavior, Elsevier, vol. 71(2), pages 527-533, March.
    7. Geoffroy de Clippel, 2014. "Behavioral Implementation," American Economic Review, American Economic Association, vol. 104(10), pages 2975-3002, October.
    8. Elchanan Ben‐Porath & Eddie Dekel & Barton L. Lipman, 2019. "Mechanisms With Evidence: Commitment and Robustness," Econometrica, Econometric Society, vol. 87(2), pages 529-566, March.
    9. Kfir Eliaz, 2002. "Fault Tolerant Implementation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 69(3), pages 589-610.
    10. Kartik, Navin & Tercieux, Olivier & Holden, Richard, 2014. "Simple mechanisms and preferences for honesty," Games and Economic Behavior, Elsevier, vol. 83(C), pages 284-290.
    11. 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.
    12. , & , & ,, 2007. "Secure implementation," Theoretical Economics, Econometric Society, vol. 2(3), September.
    13. Hong, Lu, 1995. "Nash Implementation in Production Economies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(3), pages 401-417, May.
    14. Hong, Lu, 1998. "Feasible Bayesian Implementation with State Dependent Feasible Sets," Journal of Economic Theory, Elsevier, vol. 80(2), pages 201-221, June.
    15. Tumennasan, Norovsambuu, 2013. "To err is human: Implementation in quantal response equilibria," Games and Economic Behavior, Elsevier, vol. 77(1), pages 138-152.
    16. , & ,, 2012. "Implementation with evidence," Theoretical Economics, Econometric Society, vol. 7(2), May.
    17. Abreu, Dilip & Sen, Arunava, 1991. "Virtual Implementation in Nash Equilibrium," Econometrica, Econometric Society, vol. 59(4), pages 997-1021, July.
    18. L. Hurwicz, 1979. "Outcome Functions Yielding Walrasian and Lindahl Allocations at Nash Equilibrium Points," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 46(2), pages 217-225.
    19. repec:hal:pseose:halshs-00943301 is not listed on IDEAS
    20. E. Maskin, 1978. "Implementation and Strong Nash Equilibrium," Working papers 216, Massachusetts Institute of Technology (MIT), Department of Economics.
    21. Crawford, Vincent P., 2021. "Efficient mechanisms for level-k bilateral trading," Games and Economic Behavior, Elsevier, vol. 127(C), pages 80-101.
    22. 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.
    23. Arya, Anil & Glover, Jonathan & Rajan, Uday, 2000. "Implementation in Principal-Agent Models of Adverse Selection," Journal of Economic Theory, Elsevier, vol. 93(1), pages 87-109, July.
    24. Moore, John & Repullo, Rafael, 1988. "Subgame Perfect Implementation," Econometrica, Econometric Society, vol. 56(5), pages 1191-1220, September.
    25. Kneeland, Terri, 2022. "Mechanism design with level-k types: Theory and an application to bilateral trade," Journal of Economic Theory, Elsevier, vol. 201(C).
    26. A. Michael Spence, 1980. "Multi-Product Quantity-Dependent Prices and Profitability Constraints," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 47(5), pages 821-841.
    27. Schmeidler, David, 1980. "Walrasian Analysis via Strategic Outcome Functions," Econometrica, Econometric Society, vol. 48(7), pages 1585-1593, November.
    28. Abreu Dilip & Matsushima Hitoshi, 1994. "Exact Implementation," Journal of Economic Theory, Elsevier, vol. 64(1), pages 1-19, October.
    29. Hayashi, Takashi & Lombardi, Michele, 2017. "Implementation in partial equilibrium," Journal of Economic Theory, Elsevier, vol. 169(C), pages 13-34.
    30. Mirrlees, J. A., 1976. "Optimal tax theory : A synthesis," Journal of Public Economics, Elsevier, vol. 6(4), pages 327-358, November.
    31. Saijo, Tatsuyoshi & Yamato, Takehiko, 2007. "Secure Implementation―Theory and Experiments―," Economic Review, Hitotsubashi University, vol. 58(2), pages 122-135, April.
    32. Hayashi, Takashi & Lombardi, Michele, 2019. "Constrained implementation," Journal of Economic Theory, Elsevier, vol. 183(C), pages 546-567.
    33. repec:hal:pseose:halshs-00754592 is not listed on IDEAS
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    More about this item

    Keywords

    Comonotonicity; mechanism design; implementation; robustness; resilience; safe implementation; safety no-veto;
    All these keywords.

    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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