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Separability and decomposition in mechanism design with transfers

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  • Mishra, Debasis
  • Nath, Swaprava
  • Roy, Souvik

Abstract

In private values quasi-linear environment, we consider problems where allocation decisions along multiple components have to be made. Every agent has additively separable valuation over the components. We show that every unanimous and dominant strategy implementable allocation rule in this problem is a component-wise weighted utilitarian rule, which assigns non-negative weight vectors to agents in each component and chooses an alternative in each component by maximizing the weighted sum of valuations in that component. A corollary of our result is that every unanimous and dominant strategy implementable allocation rule can be almost decomposed (modulo tie-breaking) into dominant strategy implementable allocation rules along each component.

Suggested Citation

  • Mishra, Debasis & Nath, Swaprava & Roy, Souvik, 2018. "Separability and decomposition in mechanism design with transfers," Games and Economic Behavior, Elsevier, vol. 109(C), pages 240-261.
    • Handle: RePEc:eee:gamebe:v:109:y:2018:i:c:p:240-261
    DOI: 10.1016/j.geb.2017.12.018
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    References listed on IDEAS

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    1. Mishra, Debasis & Sen, Arunava, 2012. "Robertsʼ Theorem with neutrality: A social welfare ordering approach," Games and Economic Behavior, Elsevier, vol. 75(1), pages 283-298.
    2. Lars-Gunnar Svensson & Pär Torstensson, 2008. "Strategy-proof allocation of multiple public goods," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(2), pages 181-196, February.
    3. Thierry Marchant & Debasis Mishra, 2015. "Mechanism design with two alternatives in quasi-linear environments," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(2), pages 433-455, February.
    4. Ron Lavi & Ahuva Mu’alem & Noam Nisan, 2009. "Two simplified proofs for Roberts’ theorem," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 32(3), pages 407-423, March.
    5. Carbajal, Juan Carlos & McLennan, Andrew & Tourky, Rabee, 2013. "Truthful implementation and preference aggregation in restricted domains," Journal of Economic Theory, Elsevier, vol. 148(3), pages 1074-1101.
    6. John A. Weymark, 1999. "Decomposable Strategy-Proof Social Choice Functions," The Japanese Economic Review, Japanese Economic Association, vol. 50(3), pages 343-355, September.
    7. Michel Le Breton & Arunava Sen, 1999. "Separable Preferences, Strategyproofness, and Decomposability," Econometrica, Econometric Society, vol. 67(3), pages 605-628, May.
    8. Barbera, Salvador & Sonnenschein, Hugo & Zhou, Lin, 1991. "Voting by Committees," Econometrica, Econometric Society, vol. 59(3), pages 595-609, May.
    9. Philippe Jehiel & Moritz Meyer-ter-Vehn & Benny Moldovanu, 2008. "Ex-post implementation and preference aggregation via potentials," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 37(3), pages 469-490, December.
    10. Le Breton, Michel & Weymark, John A., 1999. "Strategy-proof social choice with continuous separable preferences," Journal of Mathematical Economics, Elsevier, vol. 32(1), pages 47-85, August.
    11. Reny, Philip J., 2001. "Arrow's theorem and the Gibbard-Satterthwaite theorem: a unified approach," Economics Letters, Elsevier, vol. 70(1), pages 99-105, January.
    12. Barbera Salvador & Gul Faruk & Stacchetti Ennio, 1993. "Generalized Median Voter Schemes and Committees," Journal of Economic Theory, Elsevier, vol. 61(2), pages 262-289, December.
    13. Salvador Barberà, 2010. "Strategy-proof social choice," UFAE and IAE Working Papers 828.10, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    14. Debasis Mishra & Abdul Quadir, 2014. "Non-bossy single object auctions," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(1), pages 93-110, April.
    15. , & ,, 2007. "A non-differentiable approach to revenue equivalence," Theoretical Economics, Econometric Society, vol. 2(4), December.
    16. 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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    More about this item

    Keywords

    Separable types; Affine maximizer; Roberts' theorem;
    All these keywords.

    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design

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