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Robust Implementation in General Mechanisms

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Abstract

A social choice function is robustly implemented if every equilibrium on every type space achieves outcomes consistent with it. We identify a robust monotonicity condition that is necessary and (with mild extra assumptions) sufficient for robust implementation. Robust monotonicity is strictly stronger than both Maskin monotonicity (necessary and almost sufficient for complete information implementation) and ex post monotonicity (necessary and almost sufficient for ex post implementation). It is equivalent to Bayesian monotonicity on all type spaces.

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  • Dirk Bergemann & Stephen Morris, 2008. "Robust Implementation in General Mechanisms," Cowles Foundation Discussion Papers 1666, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1666
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    1. Kim-Sau Chung & Jeffrey C. Ely, 2000. "Efficient and Dominance Solvable Auctions with Interdependent Valuations," Discussion Papers 1313, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    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. Palfrey, Thomas R & Srivastava, Sanjay, 1989. "Mechanism Design with Incomplete Information: A Solution to the Implementation Problem," Journal of Political Economy, University of Chicago Press, vol. 97(3), pages 668-691, June.
    4. Bergemann, Dirk & Morris, Stephen, 2008. "Ex post implementation," Games and Economic Behavior, Elsevier, vol. 63(2), pages 527-566, July.
    5. Dirk Bergemann & Stephen Morris, 2005. "Robust Mechanism Design," Econometrica, Econometric Society, vol. 73(6), pages 1771-1813, November.
    6. Battigalli Pierpaolo & Siniscalchi Marciano, 2003. "Rationalization and Incomplete Information," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 3(1), pages 1-46, June.
    7. Adam Brandenburger & Eddie Dekel, 2014. "Rationalizability and Correlated Equilibria," World Scientific Book Chapters,in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 3, pages 43-57 World Scientific Publishing Co. Pte. Ltd..
    8. 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.
    9. Jackson, Matthew O, 1991. "Bayesian Implementation," Econometrica, Econometric Society, vol. 59(2), pages 461-477, March.
    10. Matthew O. Jackson, 1992. "Implementation in Undominated Strategies: A Look at Bounded Mechanisms," Review of Economic Studies, Oxford University Press, vol. 59(4), pages 757-775.
    11. John Duggan, 1997. "Virtual Bayesian Implementation," Econometrica, Econometric Society, vol. 65(5), pages 1175-1200, September.
    12. Abreu, Dilip & Matsushima, Hitoshi, 1992. "A Response [Virtual Implementation in Iteratively Undominated Strategies I: Complete Information]," Econometrica, Econometric Society, vol. 60(6), pages 1439-1442, November.
    13. Bergemann, Dirk & Morris, Stephen, 2011. "Robust implementation in general mechanisms," Games and Economic Behavior, Elsevier, vol. 71(2), pages 261-281, March.
    14. Serrano, Roberto & Vohra, Rajiv, 2005. "A characterization of virtual Bayesian implementation," Games and Economic Behavior, Elsevier, vol. 50(2), pages 312-331, February.
    15. 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.
    16. Dekel, Eddie & Fudenberg, Drew & Morris, Stephen, 2007. "Interim correlated rationalizability," Theoretical Economics, Econometric Society, vol. 2(1), pages 15-40, March.
    17. Dirk Bergemann & Stephen Morris, 2009. "Robust Implementation in Direct Mechanisms," Review of Economic Studies, Oxford University Press, vol. 76(4), pages 1175-1204.
    18. Lipman Barton L., 1994. "A Note on the Implications of Common Knowledge of Rationality," Games and Economic Behavior, Elsevier, vol. 6(1), pages 114-129, January.
    19. Gale, David, 1989. "The Theory of Linear Economic Models," University of Chicago Press Economics Books, University of Chicago Press, edition 1, number 9780226278841, July.
    20. Postlewaite, Andrew & Schmeidler, David, 1986. "Implementation in differential information economies," Journal of Economic Theory, Elsevier, vol. 39(1), pages 14-33, June.
    21. Bergemann, Dirk & Morris, Stephen, 2009. "Robust virtual implementation," Theoretical Economics, Econometric Society, vol. 4(1), March.
    22. 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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    Cited by:

    1. 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..
    2. Shimoji, Makoto & Schweinzer, Paul, 2015. "Implementation without incentive compatibility: Two stories with partially informed planners," Games and Economic Behavior, Elsevier, vol. 91(C), pages 258-267.
    3. Tilman Borgers & Doug Smith, 2012. "Robustly Ranking Mechanisms," American Economic Review, American Economic Association, vol. 102(3), pages 325-329, May.
    4. Rodrigo A. Velez & Alexander L. Brown, 2018. "Empirical Equilibrium," Papers 1804.07986, arXiv.org.
    5. Bergemann, Dirk & Morris, Stephen, 2011. "Robust implementation in general mechanisms," Games and Economic Behavior, Elsevier, vol. 71(2), pages 261-281, March.
    6. repec:spr:etbull:v:3:y:2015:i:2:d:10.1007_s40505-014-0050-8 is not listed on IDEAS
    7. Yu Chen & Zhenhua Wu, 2012. "Delegation Principle for Multi-agency Games under Ex Post Equilibrium," Caepr Working Papers 2012-008, Center for Applied Economics and Policy Research, Economics Department, Indiana University Bloomington.
    8. Ghossoub, Mario, 2010. "Belief heterogeneity in the Arrow-Borch-Raviv insurance model," MPRA Paper 37630, University Library of Munich, Germany, revised 22 Mar 2012.
    9. de Castro, Luciano I. & Liu, Zhiwei & Yannelis, Nicholas C., 2017. "Implementation under ambiguity," Games and Economic Behavior, Elsevier, vol. 101(C), pages 20-33.
    10. Penta, Antonio, 2015. "Robust dynamic implementation," Journal of Economic Theory, Elsevier, vol. 160(C), pages 280-316.
    11. Adachi, Tsuyoshi, 2014. "Robust and secure implementation: equivalence theorems," Games and Economic Behavior, Elsevier, vol. 86(C), pages 96-101.
    12. Müller, Christoph, 2016. "Robust virtual implementation under common strong belief in rationality," Journal of Economic Theory, Elsevier, vol. 162(C), pages 407-450.
    13. repec:inu:caeprp:2012-008 is not listed on IDEAS
    14. Artemov, Georgy & Kunimoto, Takashi & Serrano, Roberto, 2013. "Robust virtual implementation: Toward a reinterpretation of the Wilson doctrine," Journal of Economic Theory, Elsevier, vol. 148(2), pages 424-447.
    15. Yamashita, Takuro, 2015. "Strategic and structural uncertainty in robust implementation," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 267-279.
    16. Kyungmin Kim & Antonio Penta, 2012. "A Robustly Efficient Auction," Carlo Alberto Notebooks 248, Collegio Carlo Alberto.

    More about this item

    Keywords

    Mechanism design; Implementation; Robustness; Common knowledge; Interim equilibrium; Dominant strategies;

    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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