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On the equivalence of Bayesian and dominant strategy implementation for environments with nonlinear utilities

Author

Listed:
  • Alexey Kushnir

    (Carnegie Mellon University)

  • Shuo Liu

    (University of Zurich)

Abstract

We extend the equivalence between Bayesian and dominant strategy implementation (Manelli and Vincent in Econometrica 78:1905–1938, 2010; Gershkov et al. in Econometrica 81: 197–220, 2013) to environments with nonlinear utilities satisfying a property of increasing differences over distributions and a convex-valued assumption. The new equivalence result produces novel implications to the literature on the principal-agent problem with allocative externalities, environmental mechanism design, and public good provision.

Suggested Citation

  • Alexey Kushnir & Shuo Liu, 2019. "On the equivalence of Bayesian and dominant strategy implementation for environments with nonlinear utilities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(3), pages 617-644, April.
    • Handle: RePEc:spr:joecth:v:67:y:2019:i:3:d:10.1007_s00199-018-1124-x
    DOI: 10.1007/s00199-018-1124-x
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    1. David Martimort & Wilfried Sand‐Zantman, 2013. "Solving the global warming problem: beyond markets, simple mechanisms may help!," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 46(2), pages 361-378, May.
    2. Gorkem Celik, 2015. "Implementation by Gradual Revelation," RAND Journal of Economics, RAND Corporation, vol. 46(2), pages 271-296, June.
    3. Mishra, Debasis & Pramanik, Anup & Roy, Souvik, 2014. "Multidimensional mechanism design in single peaked type spaces," Journal of Economic Theory, Elsevier, vol. 153(C), pages 103-116.
    4. Ilya Segal, 2003. "Optimal Pricing Mechanisms with Unknown Demand," American Economic Review, American Economic Association, vol. 93(3), pages 509-529, June.
    5. Philippe Jehiel & Benny Moldovanu, 2005. "Allocative and Informational Externalities in Auctions and Related Mechanisms," Levine's Bibliography 784828000000000490, UCLA Department of Economics.
    6. Jehiel, Philippe & Moldovanu, Benny & Stacchetti, Ennio, 1996. "How (Not) to Sell Nuclear Weapons," American Economic Review, American Economic Association, vol. 86(4), pages 814-829, September.
    7. Shuo Liu & Harry Pei, 2017. "Monotone equilibria in signalling games," ECON - Working Papers 252, Department of Economics - University of Zurich.
    8. David Martimort & Wilfried Sand-Zantman, 2016. "A Mechanism Design Approach To Climate-Change Agreements," Journal of the European Economic Association, European Economic Association, vol. 14(3), pages 669-718, June.
    9. Kushnir, Alexey, 2015. "On sufficiency of dominant strategy implementation in environments with correlated types," Economics Letters, Elsevier, vol. 133(C), pages 4-6.
    10. 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..
    11. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    12. Sushil Bikhchandani & Shurojit Chatterji & Ron Lavi & Ahuva Mu'alem & Noam Nisan & Arunava Sen, 2006. "Weak Monotonicity Characterizes Deterministic Dominant-Strategy Implementation," Econometrica, Econometric Society, vol. 74(4), pages 1109-1132, July.
    13. Tilman Börgers & Peter Norman, 2009. "A note on budget balance under interim participation constraints: the case of independent types," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 39(3), pages 477-489, June.
    14. George J. Mailath & Andrew Postlewaite, 1990. "Asymmetric Information Bargaining Problems with Many Agents," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 57(3), pages 351-367.
    15. John K.‐H. Quah & Bruno Strulovici, 2012. "Aggregating the Single Crossing Property," Econometrica, Econometric Society, vol. 80(5), pages 2333-2348, September.
    16. Martin F. Hellwig, 2003. "Public-Good Provision with Many Participants," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 70(3), pages 589-614.
    17. Dilip Mookherjee & Masatoshi Tsumagari, 2004. "The Organization of Supplier Networks: Effects of Delegation and Intermediation," Econometrica, Econometric Society, vol. 72(4), pages 1179-1219, July.
    18. Jean-Jacques Laffont & David Martimort, 1997. "Collusion under Asymmetric Information," Econometrica, Econometric Society, vol. 65(4), pages 875-912, July.
    19. Baliga, Sandeep & Maskin, Eric, 2003. "Mechanism design for the environment," Handbook of Environmental Economics, in: K. G. Mäler & J. R. Vincent (ed.), Handbook of Environmental Economics, edition 1, volume 1, chapter 7, pages 305-324, Elsevier.
    20. Mookherjee, Dilip & Reichelstein, Stefan, 1992. "Dominant strategy implementation of Bayesian incentive compatible allocation rules," Journal of Economic Theory, Elsevier, vol. 56(2), pages 378-399, April.
    21. Crawford, Vincent P, 1982. "A Theory of Disagreement in Bargaining," Econometrica, Econometric Society, vol. 50(3), pages 607-637, May.
    22. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, vol. 70(2), pages 583-601, March.
    23. Alexey Kushnir, 2013. "On the equivalence between Bayesian and dominant strategy implementation: the case of correlated types," ECON - Working Papers 129, Department of Economics - University of Zurich.
    24. Peter Norman, 2004. "Efficient Mechanisms for Public Goods with Use Exclusions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 71(4), pages 1163-1188.
    25. K. G. Mäler & J. R. Vincent (ed.), 2003. "Handbook of Environmental Economics," Handbook of Environmental Economics, Elsevier, edition 1, volume 1, number 1.
    26. Ilya Segal, 1999. "Contracting with Externalities," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(2), pages 337-388.
    27. Itai Ashlagi & Mark Braverman & Avinatan Hassidim & Dov Monderer, 2010. "Monotonicity and Implementability," Econometrica, Econometric Society, vol. 78(5), pages 1749-1772, September.
    28. Alex Gershkov & Jacob K. Goeree & Alexey Kushnir & Benny Moldovanu & Xianwen Shi, 2013. "On the Equivalence of Bayesian and Dominant Strategy Implementation," Econometrica, Econometric Society, vol. 81(1), pages 197-220, January.
    29. John O. Ledyard & Thomas R. Palfrey, 1999. "A Characterization of Interim Efficiency with Public Goods," Econometrica, Econometric Society, vol. 67(2), pages 435-448, March.
    30. Alexey Kushnir & Shuo Liu, 2017. "On linear transformations of intersections," ECON - Working Papers 255, Department of Economics - University of Zurich.
    31. Izak Duenyas & Bin Hu & Damian R. Beil, 2013. "Simple Auctions for Supply Contracts," Management Science, INFORMS, vol. 59(10), pages 2332-2342, October.
    32. repec:hal:pseose:halshs-00833194 is not listed on IDEAS
    33. Sergei Severinov, 2008. "The value of information and optimal organization," RAND Journal of Economics, RAND Corporation, vol. 39(1), pages 238-265, March.
    34. Jacob K. Goeree & Alexey Kushnir, 2011. "A geometric approach to mechanism design," ECON - Working Papers 056, Department of Economics - University of Zurich, revised Jun 2013.
    35. Rochet, Jean-Charles, 1987. "A necessary and sufficient condition for rationalizability in a quasi-linear context," Journal of Mathematical Economics, Elsevier, vol. 16(2), pages 191-200, April.
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    Cited by:

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    4. Rabah Amir, 2019. "Supermodularity and Complementarity in Economic Theory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(3), pages 487-496, April.
    5. Zhiwei Liu & Nicholas C. Yannelis, 2021. "Persuasion in an asymmetric information economy: a justification of Wald’s maxmin preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(3), pages 801-833, October.
    6. Liu, Shuo & Pei, Harry, 2020. "Monotone equilibria in signaling games," European Economic Review, Elsevier, vol. 124(C).
    7. Erya Yang, 2021. "Reduced-form mechanism design and ex post fairness constraints," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(2), pages 269-293, October.

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    More about this item

    Keywords

    Bayesian implementation; Dominant strategy implementation; Mechanism design; Nonlinear utilities; Increasing differences over distributions;
    All these keywords.

    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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