Mechanism Design for the truthful elicitation of costly probabilistic estimates in Distributed Information Systems
AbstractThis 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)  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.
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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 43324.
Date of creation: Oct 2010
Date of revision:
Publication status: Published in Artificial Intelligence 2.175(2011): pp. 648-672
Multiagent systems; Scoring rules; Auction theory; Mechanism design;
Find related papers by JEL classification:
- D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
- D44 - Microeconomics - - Market Structure and Pricing - - - Auctions
- D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Wolfers, Justin & Zitzewitz, Eric, 2004.
- Justin Wolfers & Eric Zitzewitz, 2004. "Prediction Markets," Discussion Papers 03-025, Stanford Institute for Economic Policy Research.
- Wolfers, Justin & Zitzewitz, Eric, 2004. "Prediction Markets," Research Papers 1854, Stanford University, Graduate School of Business.
- Justin Wolfers & Eric Zitzewitz, 2004. "Prediction Markets," NBER Working Papers 10504, National Bureau of Economic Research, Inc.
- Sanford J Grossman & Oliver D Hart, 2001.
"An Analysis of the Principal-Agent Problem,"
Levine's Working Paper Archive
391749000000000339, David K. Levine.
- Sanford Grossman & Oliver Hart, . "An Analysis of the Principal-Agent Problem," Rodney L. White Center for Financial Research Working Papers 15-80, Wharton School Rodney L. White Center for Financial Research.
- Claudio Mezzetti, 2005.
"Mechanism Design with Interdependent Valuations: Surplus Extraction,"
Discussion Papers in Economics
05/1, Department of Economics, University of Leicester, revised Mar 2006.
- Claudio Mezzetti, 2007. "Mechanism Design with Interdependent Valuations: Surplus Extraction," Economic Theory, Springer, vol. 31(3), pages 473-488, June.
- Philippe Jehiel & Benny Moldovanu, 1998.
"Efficient Design with Interdependent Valuations,"
1244, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Jehiel, Phillipe & Moldovanu, Benny, 1998. "Efficient Design with Interdependent Valuations," Sonderforschungsbereich 504 Publications 98-22, Sonderforschungsbereich 504, Universität Mannheim & Sonderforschungsbereich 504, University of Mannheim.
- Jehiel, Phillipe & Moldovanu, Benny, 1999. "Efficient Design with Interdependent Valuations," Sonderforschungsbereich 504 Publications 99-74, Sonderforschungsbereich 504, Universität Mannheim & Sonderforschungsbereich 504, University of Mannheim.
- Claudio Mezzetti, 2004. "Mechanism Design with Interdependent Valuations: Efficiency," Econometrica, Econometric Society, vol. 72(5), pages 1617-1626, 09.
- Reinhard Selten, 1998.
"Axiomatic Characterization of the Quadratic Scoring Rule,"
Springer, vol. 1(1), pages 43-61, June.
- Selten, Reinhard, 1996. "Axiomatic Characterization of the Quadratic Scoring Rule," Discussion Paper Serie B 390, University of Bonn, Germany.
- 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.
- 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.
- Groves, Theodore, 1973. "Incentives in Teams," Econometrica, Econometric Society, vol. 41(4), pages 617-31, July.
- repec:reg:rpubli:259 is not listed on IDEAS
- 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.
- 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.
- Robert Day & Paul Milgrom, 2008. "Core-selecting package auctions," International Journal of Game Theory, Springer, vol. 36(3), pages 393-407, March.
- James E. Matheson & Robert L. Winkler, 1976. "Scoring Rules for Continuous Probability Distributions," Management Science, INFORMS, vol. 22(10), pages 1087-1096, June.
- Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
- William Vickrey, 1961. "Counterspeculation, Auctions, And Competitive Sealed Tenders," Journal of Finance, American Finance Association, vol. 16(1), pages 8-37, 03.
- Papakonstantinou, A. & Bogetoft, P., 2013.
"Crowd-sourcing with uncertain quality - an auction approach,"
46055, University Library of Munich, Germany.
- Papakonstantinou, A. & Bogetoft, P., 2013. "Crowd-sourcing with uncertain quality - an auction approach," MPRA Paper 44236, University Library of Munich, Germany.
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