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Mechanism design without revenue equivalence

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  • Carbajal, Juan Carlos
  • Ely, Jeffrey C.
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    Abstract

    We study mechanism design problems in quasi-linear environments where the envelope theorem and revenue equivalence principle fail due to non-convex and non-differentiable valuations. We obtain a characterization of incentive compatibility based on the Mirrlees representation of the indirect utility and a monotonicity condition on the allocation rule, which pin down the range of possible payoffs as a function of the allocation rule. To illustrate our approach we derive the optimal selling mechanism in a buyer–seller situation where the buyer is loss-averse; we find a budget-balanced, efficient mechanism in a public goods location model; and we consider a principal–agent model with ex post non-contractible actions available to the agent.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Economic Theory.

    Volume (Year): 148 (2013)
    Issue (Month): 1 ()
    Pages: 104-133

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    Handle: RePEc:eee:jetheo:v:148:y:2013:i:1:p:104-133

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    Web page: http://www.elsevier.com/locate/inca/622869

    Related research

    Keywords: Incentive compatibility; Revenue equivalence; Integral monotonicity; Revenue maximization; Loss aversion; Efficiency; Public goods; Non-contractible actions;

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    References

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    1. Itai Ashlagi & Mark Braverman & Avinatan Hassidim & Dov Monderer, 2010. "Monotonicity and Implementability," Econometrica, Econometric Society, vol. 78(5), pages 1749-1772, 09.
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    3. Matthew Rabin, 2006. "A Model of Reference-Dependent Preferences," The Quarterly Journal of Economics, MIT Press, vol. 121(4), pages 1133-1165, November.
    4. Olszewski, Wojciech & Chung, Kim-Sau, 2007. "A non-differentiable approach to revenue equivalence," Theoretical Economics, Econometric Society, vol. 2(4), December.
    5. ehiel, Philippe & Benny Moldovanu & Ennio Stacchetti, 1994. "How (not) to sell nuclear weapons," Discussion Paper Serie B 288, University of Bonn, Germany.
    6. Groves, Theodore, 1973. "Incentives in Teams," Econometrica, Econometric Society, vol. 41(4), pages 617-31, July.
    7. William Vickrey, 1961. "Counterspeculation, Auctions, And Competitive Sealed Tenders," Journal of Finance, American Finance Association, vol. 16(1), pages 8-37, 03.
    8. Heydenreich, Birgit & Müller, Rudolf & Uetz, Marc & Vohra, Rakesh, 2008. "Characterization of Revenue Equivalence," Research Memorandum 001, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    9. Carbajal, Juan Carlos, 2010. "On the uniqueness of Groves mechanisms and the payoff equivalence principle," Games and Economic Behavior, Elsevier, vol. 68(2), pages 763-772, March.
    10. Steven R. Williams, 1999. "A characterization of efficient, bayesian incentive compatible mechanisms," Economic Theory, Springer, vol. 14(1), pages 155-180.
    11. Jehiel, Philippe & Moldovanu, Benny & Stacchetti, Ennio, 1999. "Multidimensional Mechanism Design for Auctions with Externalities," Journal of Economic Theory, Elsevier, vol. 85(2), pages 258-293, April.
    12. Krishna, Vijay & Maenner, Eliot, 2001. "Convex Potentials with an Application to Mechanism Design," Econometrica, Econometric Society, vol. 69(4), pages 1113-19, July.
    13. Nenad Kos & Matthias Messner, 2010. "Extremal Incentive Compatible Transfers," Working Papers 359, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    14. Gul, Faruk, 1991. "A Theory of Disappointment Aversion," Econometrica, Econometric Society, vol. 59(3), pages 667-86, May.
    15. 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.
    16. Holmstrom, Bengt, 1979. "Groves' Scheme on Restricted Domains," Econometrica, Econometric Society, vol. 47(5), pages 1137-44, September.
    17. 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, 07.
    18. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, vol. 70(2), pages 583-601, March.
    19. Edward Clarke, 1971. "Multipart pricing of public goods," Public Choice, Springer, vol. 11(1), pages 17-33, September.
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    Cited by:
    1. Kos, Nenad & Messner, Matthias, 2013. "Incentive compatibility in non-quasilinear environments," Economics Letters, Elsevier, vol. 121(1), pages 12-14.
    2. Juan Carlos Carbajal & Andrew McLennan & Rabee Tourky, 2012. "Truthful Implementation and Preference Aggregation in Restricted Domains," Discussion Papers Series 459, School of Economics, University of Queensland, Australia.
    3. Debasis Mishra & Anup Pramanik & Souvik Roy, 2013. "Implementation in multidimensional domains with ordinal restrictions," Indian Statistical Institute, Planning Unit, New Delhi Discussion Papers 13-07, Indian Statistical Institute, New Delhi, India.

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