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Dominant Strategy Implementation with a Convex Product Space of Valuations

Author

Listed:
  • Katherine Cuff

    (Department of Economics, McMaster University)

  • Sunghoon Hong

    (Department of Economics, Vanderbilt University)

  • Jesse Schwartz

    (Department of Economics,Kennesaw State University)

  • Quan Wen

    (Department of Economics, Vanderbilt University)

  • John Weymark

    (Department of Economics, Vanderbilt University)

Abstract

A necessary and sufficient condition for dominant strategy implementability when preferences are quasilinear is that, for any individual i and any choice of the types of the other individuals, all k-cycles in i's allocation graph have nonnegative length for every integer k � 2. Saks and Yu (Proceedings of the 6th ACM Conference on Electronic Commerce (EC'05), 2005, 286-293) have shown that when the number of outcomes is finite and i's valuation type space is convex, nonnegativity of the length of all 2-cycles is sufficient for the nonnegativity of the length of all k-cycles. In this article, it is shown that if each individual's valuation type space is a convex product space and a mild domain regularity condition is satisfied, then (i) the nonnegativity of all 2-cycles implies that all k-cycles have zero length and (ii) all 2-cycles having zero length is necessary and sufficient for dominant strategy implementability.

Suggested Citation

  • Katherine Cuff & Sunghoon Hong & Jesse Schwartz & Quan Wen & John Weymark, 2011. "Dominant Strategy Implementation with a Convex Product Space of Valuations," Vanderbilt University Department of Economics Working Papers 1104, Vanderbilt University Department of Economics.
    • Handle: RePEc:van:wpaper:1104
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    References listed on IDEAS

    as
    1. 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.
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    10. Vohra,Rakesh V., 2011. "Mechanism Design," Cambridge Books, Cambridge University Press, number 9781107004368.
    11. Itai Ashlagi & Mark Braverman & Avinatan Hassidim & Dov Monderer, 2010. "Monotonicity and Implementability," Econometrica, Econometric Society, vol. 78(5), pages 1749-1772, September.
    12. 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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    Citations

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    Cited by:

    1. Paul H. Edelman & John A Weymark, 2017. "Dominant Strategy Implementability, Zero Length Cycles, and Affine Maximizers," Vanderbilt University Department of Economics Working Papers 17-00002, Vanderbilt University Department of Economics.
    2. , & ,, 2013. "Implementation in multidimensional dichotomous domains," Theoretical Economics, Econometric Society, vol. 8(2), May.
    3. Kazumura, Tomoya & Mishra, Debasis & Serizawa, Shigehiro, 2020. "Mechanism design without quasilinearity," Theoretical Economics, Econometric Society, vol. 15(2), May.
    4. Paul H. Edelman & John A Weymark, 2018. "Unrestricted Domain Extensions of Dominant Strategy Implementable Allocation Functions," Vanderbilt University Department of Economics Working Papers 18-00003, Vanderbilt University Department of Economics.
    5. Debasis Mishra & Anup Pramanik & Souvik Roy, 2013. "Implementation in multidimensional domains with ordinal restrictions," Discussion Papers 13-07, Indian Statistical Institute, Delhi.
    6. Debasis Mishra & Abdul Quadir, 2012. "Deterministic single object auctions with private values," Discussion Papers 12-06, Indian Statistical Institute, Delhi.

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    More about this item

    Keywords

    2-cycle condition; dominant strategy implementation; mechanism design; revenue equivalence; Rockafellar-Rochet Theorem; Saks-Yu Theorem;
    All these keywords.

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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