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General truthfulness characterizations via convex analysis

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  • Frongillo, Rafael M.
  • Kash, Ian A.

Abstract

We present a model of truthful elicitation which generalizes and extends mechanisms, scoring rules, and a number of related settings that do not qualify as one or the other. Our main result is a characterization theorem, yielding characterizations for all of these settings. This includes a new characterization of scoring rules for non-convex sets of distributions. We combine the characterization theorem with duality to give a simple construction to convert between scoring rules and randomized mechanisms. We also show how a generalization of this characterization gives a new proof of a mechanism design result due to Saks and Yu.

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  • Frongillo, Rafael M. & Kash, Ian A., 2021. "General truthfulness characterizations via convex analysis," Games and Economic Behavior, Elsevier, vol. 130(C), pages 636-662.
    • Handle: RePEc:eee:gamebe:v:130:y:2021:i:c:p:636-662
    DOI: 10.1016/j.geb.2021.09.010
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    1. Gneiting, Tilmann, 2011. "Making and Evaluating Point Forecasts," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 746-762.
    2. Jehiel, Philippe & Moldovanu, Benny & Stacchetti, Ennio, 1996. "How (Not) to Sell Nuclear Weapons," American Economic Review, American Economic Association, vol. 86(4), pages 814-829, September.
    3. Jehiel, Philippe & Moldovanu, Benny, 2001. "Efficient Design with Interdependent Valuations," Econometrica, Econometric Society, vol. 69(5), pages 1237-1259, September.
    4. Chambers, Christopher P. & Lambert, Nicolas S., 2014. "Dynamically Eliciting Unobservable Information," Research Papers 3036, Stanford University, Graduate School of Business.
    5. 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.
    6. Fang, Fang & Stinchcombe, Maxwell B. & Whinston, Andrew B., 2010. "Proper scoring rules with arbitrary value functions," Journal of Mathematical Economics, Elsevier, vol. 46(6), pages 1200-1210, November.
    7. Rochet, J. C., 1985. "The taxation principle and multi-time Hamilton-Jacobi equations," Journal of Mathematical Economics, Elsevier, vol. 14(2), pages 113-128, April.
    8. Muller, Rudolf & Perea, Andres & Wolf, Sascha, 2007. "Weak monotonicity and Bayes-Nash incentive compatibility," Games and Economic Behavior, Elsevier, vol. 61(2), pages 344-358, November.
    9. Robin Hanson, 2003. "Combinatorial Information Market Design," Information Systems Frontiers, Springer, vol. 5(1), pages 107-119, January.
    10. Birgit Heydenreich & Rudolf Müller & Marc Uetz & Rakesh V. Vohra, 2009. "Characterization of Revenue Equivalence," Econometrica, Econometric Society, vol. 77(1), pages 307-316, January.
    11. Gabriel Carroll, 2012. "When Are Local Incentive Constraints Sufficient?," Econometrica, Econometric Society, vol. 80(2), pages 661-686, March.
    12. 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.
    13. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, vol. 70(2), pages 583-601, March.
    14. Carbajal, Juan Carlos & Ely, Jeffrey C., 2013. "Mechanism design without revenue equivalence," Journal of Economic Theory, Elsevier, vol. 148(1), pages 104-133.
    15. Efe A. Ok, 2007. "Preliminaries of Real Analysis, from Real Analysis with Economic Applications," Introductory Chapters, in: Real Analysis with Economic Applications, Princeton University Press.
    16. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
    17. Kos, Nenad & Messner, Matthias, 2013. "Extremal incentive compatible transfers," Journal of Economic Theory, Elsevier, vol. 148(1), pages 134-164.
    18. Steffen Borgwardt & Rafael M. Frongillo, 2019. "Power Diagram Detection with Applications to Information Elicitation," Journal of Optimization Theory and Applications, Springer, vol. 181(1), pages 184-196, April.
    19. Itai Ashlagi & Mark Braverman & Avinatan Hassidim & Dov Monderer, 2010. "Monotonicity and Implementability," Econometrica, Econometric Society, vol. 78(5), pages 1749-1772, September.
    20. Krishna, Vijay & Maenner, Eliot, 2001. "Convex Potentials with an Application to Mechanism Design," Econometrica, Econometric Society, vol. 69(4), pages 1113-1119, July.
    21. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    22. McAfee, R. Preston & McMillan, John, 1988. "Multidimensional incentive compatibility and mechanism design," Journal of Economic Theory, Elsevier, vol. 46(2), pages 335-354, December.
    23. 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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    Cited by:

    1. Mark Whitmeyer, 2024. "Can One Hear the Shape of a Decision Problem?," Papers 2403.06344, arXiv.org, revised Apr 2024.
    2. Rafael Frongillo, 2022. "Quantum Information Elicitation," Papers 2203.07469, arXiv.org.
    3. Liu, Yi & Wu, Fan, 2024. "Implementing randomized allocation rules with outcome-contingent transfers," Journal of Economic Theory, Elsevier, vol. 220(C).
    4. Patrick Lahr & Axel Niemeyer, 2024. "Extreme Points in Multi-Dimensional Screening," Papers 2412.00649, arXiv.org.

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    More about this item

    Keywords

    Information elicitation; Mechanism design; Proper scoring rules; Implementability characterizations; Property elicitation; Convex analysis;
    All these keywords.

    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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