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Extremal Incentive Compatible Transfers

Author

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  • Nenad Kos
  • Matthias Messner
Abstract
We characterize the boundaries of the set of transfers implementing a given allocation rule without imposing any assumptions on the agent's type space or utility function besides quasi-linearity. In particular, we characterize the pointwise largest and the pointwise smallest transfer that implement a given allocation rule and are equal to zero at some prespecified type (extremal transfers). Exploiting the concept of extremal transfers allows us to obtain an exact characterization of the set of all implementable allocation rules (the set of transfers is non-empty) and the set of allocation rules satisfying Revenue Equivalence (the extremal transfers coincide). Furthermore, we show how the extremal transfers can be put to use in mechanism design problems where Revenue Equivalence does not hold. To this end we first explore the role of extremal transfers when the agents with type dependent outside options are free to participate in the mechanism. Finally, we consider the question of budget balanced implementation. We show that an allocation rule can be implemented in an incentive compatible, individually rational and ex post budget balanced mechanism if and only if there exists an individually rational extremal transfer scheme that delivers an ex ante budget surplus.

Suggested Citation

  • Nenad Kos & Matthias Messner, 2010. "Extremal Incentive Compatible Transfers," Working Papers 359, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    • Handle: RePEc:igi:igierp:359
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    References listed on IDEAS

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    Cited by:

    1. Frongillo, Rafael M. & Kash, Ian A., 2021. "General truthfulness characterizations via convex analysis," Games and Economic Behavior, Elsevier, vol. 130(C), pages 636-662.
    2. Nenad Kos & Matthias Messner, 2015. "Selling to the Mean," CESifo Working Paper Series 5443, CESifo.
    3. Kos, Nenad & Messner, Matthias, 2013. "Incentive compatibility in non-quasilinear environments," Economics Letters, Elsevier, vol. 121(1), pages 12-14.
    4. Rahman, David M., 2024. "Detecting profitable deviations," Journal of Mathematical Economics, Elsevier, vol. 111(C).
    5. Yamashita, Takuro & Zhu, Shuguang, 2021. "Type-contingent Information Disclosure," TSE Working Papers 21-1242, Toulouse School of Economics (TSE).
    6. Carbajal, Juan Carlos & Müller, Rudolf, 2015. "Implementability under monotonic transformations in differences," Journal of Economic Theory, Elsevier, vol. 160(C), pages 114-131.
    7. Carrasco, Vinicius & Farinha Luz, Vitor & Kos, Nenad & Messner, Matthias & Monteiro, Paulo & Moreira, Humberto, 2018. "Optimal selling mechanisms under moment conditions," Journal of Economic Theory, Elsevier, vol. 177(C), pages 245-279.
    8. Mehmet Ekmekci & Nenad Kos & Rakesh Vohra, 2016. "Just Enough or All: Selling a Firm," American Economic Journal: Microeconomics, American Economic Association, vol. 8(3), pages 223-256, August.
    9. Dilip Mookherjee & Masatoshi Tsumagari, 2014. "Mechanism Design with Communication Constraints," Journal of Political Economy, University of Chicago Press, vol. 122(5), pages 1094-1129.
    10. Dworczak, Piotr & Zhang, Anthony Lee, 2017. "Implementability, Walrasian equilibria, and efficient matchings," Economics Letters, Elsevier, vol. 153(C), pages 57-60.
    11. Alfredo Di Tillio & Nenad Kos & Matthias Messner, 2012. "The Design of Ambiguous Mechanisms," Working Papers 446, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    12. Rohit Lamba, 2022. "Efficiency with(out) intermediation in repeated bilateral trade," Papers 2202.04201, arXiv.org.
    13. Rahul Deb & Debasis Mishra, 2014. "Implementation With Contingent Contracts," Econometrica, Econometric Society, vol. 82, pages 2371-2393, November.
    14. Carbajal, Juan Carlos & Müller, Rudolf, 2017. "Monotonicity and revenue equivalence domains by monotonic transformations in differences," Journal of Mathematical Economics, Elsevier, vol. 70(C), pages 29-35.
    15. 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.
    16. , & ,, 2013. "Implementation in multidimensional dichotomous domains," Theoretical Economics, Econometric Society, vol. 8(2), May.
    17. Chen, Yi-Chun & Li, Jiangtao, 2018. "Revisiting the foundations of dominant-strategy mechanisms," Journal of Economic Theory, Elsevier, vol. 178(C), pages 294-317.
    18. Piotr Dworczak, 2020. "Mechanism Design With Aftermarkets: Cutoff Mechanisms," Econometrica, Econometric Society, vol. 88(6), pages 2629-2661, November.
    19. Carbajal, Juan Carlos & Ely, Jeffrey C., 2013. "Mechanism design without revenue equivalence," Journal of Economic Theory, Elsevier, vol. 148(1), pages 104-133.
    20. Debasis Mishra & Anup Pramanik & Souvik Roy, 2013. "Implementation in multidimensional domains with ordinal restrictions," Discussion Papers 13-07, Indian Statistical Institute, Delhi.
    21. Berger, A. & Müller, R.J. & Naeemi, S.H., 2010. "Path-monotonicity and incentive compatibility," Research Memorandum 035, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).

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    More about this item

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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