IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/43324.html
   My bibliography  Save this paper

Mechanism Design for the truthful elicitation of costly probabilistic estimates in Distributed Information Systems

Author

Listed:
  • Papakonstantinou, A.
  • Rogers, A
  • Gerding, E. H.
  • Jennings, N. R.

Abstract

This paper reports on the design of a novel two-stage mechanism, based on strictly proper scoring rules, that allows a centre to acquire a costly forecast of a future event (such as a meteorological phenomenon) or a probabilistic estimate of a specific parameter (such as the quality of an expected service), with a specified minimum precision, from one or more agents. In the first stage, the centre elicits the agents' true costs and identifies the agent that can provide an estimate of the specified precision at the lowest cost. Then, in the second stage, the centre uses an appropriately scaled strictly proper scoring rule to incentivise this agent to generate the estimate with the required precision, and to truthfully report it. In particular, this is the first mechanism that can be applied to settings in which the centre has no knowledge about the actual costs involved in the generation an agents' estimates and also has no external means of evaluating the quality and accuracy of the estimates it receives. En route to this mechanism, we first consider a setting in which any single agent can provide an estimate of the required precision, and the centre can evaluate this estimate by comparing it with the outcome which is observed at a later stage. This mechanism is then extended, so that it can be applied in a setting where the agents' different capabilities are reflected in the maximum precision of the estimates that they can provide, potentially requiring the centre to select multiple agents and combine their individual results in order to obtain an estimate of the required precision. For all three mechanisms (the original and the two extensions), we prove their economic properties (i.e. incentive compatibility and individual rationality) and then perform a number of numerical simulations. For the single agent mechanism we compare the quadratic, spherical and logarithmic scoring rules with a parametric family of scoring rules. We show that although the logarithmic scoring rule minimises both the mean and variance of the centre's total payments, using this rule means that an agent may face an unbounded penalty if it provides an estimate of extremely poor quality. We show that this is not the case for the parametric family, and thus, we suggest that the parametric scoring rule is the best candidate in our setting. Furthermore, we show that the 'multiple agent' extension describes a family of possible approaches to select agents in the first stage of our mechanism, and we show empirically and prove analytically that there is one approach that dominates all others. Finally, we compare our mechanism to the peer prediction mechanism introduced by Miller et al. (2007) [29] and show that the centre's total expected payment is the same in both mechanisms (and is equal to total expected payment in the case that the estimates can be compared to the actual outcome), while the variance in these payments is significantly reduced within our mechanism.

Suggested Citation

  • Papakonstantinou, A. & Rogers, A & Gerding, E. H. & Jennings, N. R., 2010. "Mechanism Design for the truthful elicitation of costly probabilistic estimates in Distributed Information Systems," MPRA Paper 43324, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:43324
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/43324/1/MPRA_paper_43324.pdf
    File Function: original version
    Download Restriction: no

    References listed on IDEAS

    as
    1. repec:reg:rpubli:259 is not listed on IDEAS
    2. James E. Matheson & Robert L. Winkler, 1976. "Scoring Rules for Continuous Probability Distributions," Management Science, INFORMS, vol. 22(10), pages 1087-1096, June.
    3. Jehiel, Philippe & Moldovanu, Benny, 2001. "Efficient Design with Interdependent Valuations," Econometrica, Econometric Society, vol. 69(5), pages 1237-1259, September.
    4. Claudio Mezzetti, 2007. "Mechanism Design with Interdependent Valuations: Surplus Extraction," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 31(3), pages 473-488, June.
    5. Krishna, Vijay, 2009. "Auction Theory," Elsevier Monographs, Elsevier, edition 2, number 9780123745071.
    6. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    7. Yokoo, Makoto & Sakurai, Yuko & Matsubara, Shigeo, 2004. "The effect of false-name bids in combinatorial auctions: new fraud in internet auctions," Games and Economic Behavior, Elsevier, vol. 46(1), pages 174-188, January.
    8. Justin Wolfers & Eric Zitzewitz, 2004. "Prediction Markets," Journal of Economic Perspectives, American Economic Association, vol. 18(2), pages 107-126, Spring.
    9. Robert Day & Paul Milgrom, 2008. "Core-selecting package auctions," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(3), pages 393-407, March.
    10. Robin Hanson, 2007. "Logarithmic Market Scoring Rules for Modular Combinatorial Information Aggregation," Journal of Prediction Markets, University of Buckingham Press, vol. 1(1), pages 3-15, February.
    11. Grossman, Sanford J & Hart, Oliver D, 1983. "An Analysis of the Principal-Agent Problem," Econometrica, Econometric Society, vol. 51(1), pages 7-45, January.
    12. Papakonstantinou, A. & Rogers, A. & Gerding, E. H & Jennings, N. R., 2010. "Mechanism Design for eliciting probabilistic estimates from multiple suppliers with unknown costs and limited precision," MPRA Paper 43323, University Library of Munich, Germany.
    13. William Vickrey, 1961. "Counterspeculation, Auctions, And Competitive Sealed Tenders," Journal of Finance, American Finance Association, vol. 16(1), pages 8-37, March.
    14. Papakonstantinou, A. & Rogers, A. & Gerding, E. H. & Jennings, N. R, 2008. "A Truthful Two-Stage Mechanism for Eliciting Probabilistic Estimates with Unknown Costs," MPRA Paper 43320, University Library of Munich, Germany.
    15. Reinhard Selten, 1998. "Axiomatic Characterization of the Quadratic Scoring Rule," Experimental Economics, Springer;Economic Science Association, vol. 1(1), pages 43-61, June.
    16. Groves, Theodore, 1973. "Incentives in Teams," Econometrica, Econometric Society, vol. 41(4), pages 617-631, July.
    17. Claudio Mezzetti, 2004. "Mechanism Design with Interdependent Valuations: Efficiency," Econometrica, Econometric Society, vol. 72(5), pages 1617-1626, September.
    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. Papakonstantinou, A. & Bogetoft, P., 2013. "Crowd-sourcing with uncertain quality - an auction approach," MPRA Paper 46055, University Library of Munich, Germany.

    More about this item

    Keywords

    Multiagent systems; Scoring rules; Auction theory; Mechanism design;

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • 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:pra:mprapa:43324. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Joachim Winter) or (Rebekah McClure). General contact details of provider: http://edirc.repec.org/data/vfmunde.html .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.