IDEAS home Printed from https://ideas.repec.org/p/van/wpaper/1104.html
   My bibliography  Save this paper

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
    as

    Download full text from publisher

    File URL: http://www.accessecon.com/pubs/VUECON/vu11-w04.pdf
    File Function: First version, May 2011
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. Vohra,Rakesh V., 2011. "Mechanism Design," Cambridge Books, Cambridge University Press, number 9781107004368, September.
    3. 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.
    4. Krishna, Vijay, 2009. "Auction Theory," Elsevier Monographs, Elsevier, edition 2, number 9780123745071.
    5. Birgit Heydenreich & Rudolf Müller & Marc Uetz & Rakesh V. Vohra, 2009. "Characterization of Revenue Equivalence," Econometrica, Econometric Society, vol. 77(1), pages 307-316, January.
    6. 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.
    7. EHLERS, Lars & MAJUMDAR, Dipjyoti & MISHRA, Debasis & SEN, Arunava, 2016. "Continuity and incentive compatibility," Cahiers de recherche 2016-04, Universite de Montreal, Departement de sciences economiques.
    8. William Vickrey, 1961. "Counterspeculation, Auctions, And Competitive Sealed Tenders," Journal of Finance, American Finance Association, vol. 16(1), pages 8-37, March.
    9. Itai Ashlagi & Mark Braverman & Avinatan Hassidim & Dov Monderer, 2010. "Monotonicity and Implementability," Econometrica, Econometric Society, vol. 78(5), pages 1749-1772, September.
    10. Vohra,Rakesh V., 2011. "Mechanism Design," Cambridge Books, Cambridge University Press, number 9780521179461, September.
    11. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Carbajal, Juan Carlos & Ely, Jeffrey C., 2013. "Mechanism design without revenue equivalence," Journal of Economic Theory, Elsevier, vol. 148(1), pages 104-133.
    2. 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.
    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. 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.
    5. Kazumura, Tomoya & Mishra, Debasis & Serizawa, Shigehiro, 2020. "Mechanism design without quasilinearity," Theoretical Economics, Econometric Society, vol. 15(2), May.
    6. Paul H. Edelman & John A. Weymark, 2021. "Dominant strategy implementability and zero length cycles," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(4), pages 1091-1120, November.
    7. 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.
    8. , & ,, 2013. "Implementation in multidimensional dichotomous domains," Theoretical Economics, Econometric Society, vol. 8(2), May.
    9. Rahul Deb & Debasis Mishra, 2013. "Implementation with securities," Discussion Papers 13-05, Indian Statistical Institute, Delhi.
    10. 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).
    11. 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.
    12. Debasis Mishra & Anup Pramanik & Souvik Roy, 2013. "Implementation in multidimensional domains with ordinal restrictions," Discussion Papers 13-07, Indian Statistical Institute, Delhi.
    13. Frongillo, Rafael M. & Kash, Ian A., 2021. "General truthfulness characterizations via convex analysis," Games and Economic Behavior, Elsevier, vol. 130(C), pages 636-662.
    14. Jacob K. Goeree & Alexey Kushnir, 2011. "On the equivalence of Bayesian and dominant strategy implementation in a general class of social choice problems," ECON - Working Papers 021, Department of Economics - University of Zurich.
    15. Archer, Aaron & Kleinberg, Robert, 2014. "Truthful germs are contagious: A local-to-global characterization of truthfulness," Games and Economic Behavior, Elsevier, vol. 86(C), pages 340-366.
    16. M. Yenmez, 2015. "Incentive compatible market design with applications," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(3), pages 543-569, August.
    17. Heydenreich, B. & Mishra, D. & Müller, R.J. & Uetz, M.J., 2008. "Optimal mechanisms for single machine scheduling," Research Memorandum 033, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    18. Levent Ulku, 2012. "Nonmonotone Mechanism Design," Working Papers 1202, Centro de Investigacion Economica, ITAM.
    19. Rahman, David M., 2024. "Detecting profitable deviations," Journal of Mathematical Economics, Elsevier, vol. 111(C).
    20. Yoon, Kiho, 2020. "Implementability with contingent contracts," Economics Letters, Elsevier, vol. 188(C).

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:van:wpaper:1104. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: John P. Conley (email available below). General contact details of provider: http://www.vanderbilt.edu/econ/wparchive/index.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.