A Truthful Two-Stage Mechanism for Eliciting Probabilistic Estimates with Unknown Costs
AbstractThis paper reports on the design of a novel two-stage mechanism, based on strictly proper scoring rules, that motivates selfish rational agents to make a costly probabilistic estimate or forecast of a specified precision and report it truthfully to a centre. Our mechanism is applied in a setting where the centre is faced with multiple agents, and has no knowledge about their costs. Thus, in the first stage of the mechanism, the centre uses a reverse second price auction to allocate the estimation task to the agent who reveals the lowest cost. While, in the second stage, the centre issues a payment based on a strictly proper scoring rule. When taken together, the two stages motivate agents to reveal their true costs, and then to truthfully reveal their estimate. We prove that this mechanism is incentive compatible and individually rational, and then present empirical results comparing the performance of the well known quadratic, spherical and logarithmic scoring rules. We show that the quadratic and the logarithmic rules result in the centre making the highest and the lowest expected payment to agents respectively. At the same time, however, the payments of the latter rule are unbounded, and thus the spherical rule proves to be the best candidate in this setting.
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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 43320.
Date of creation: 2008
Date of revision:
mechanism design; computer science; artificial intelligence; multi-agent systems; scoring rules;
Find related papers by JEL classification:
- D44 - Microeconomics - - Market Structure and Pricing - - - Auctions
- D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
- D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search, Learning, and Information
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.:
- James E. Matheson & Robert L. Winkler, 1976. "Scoring Rules for Continuous Probability Distributions," Management Science, INFORMS, INFORMS, vol. 22(10), pages 1087-1096, June.
- Reinhard Selten, 1998.
"Axiomatic Characterization of the Quadratic Scoring Rule,"
Experimental Economics, Springer,
Springer, vol. 1(1), pages 43-61, June.
- Selten, Reinhard, 1996. "Axiomatic Characterization of the Quadratic Scoring Rule," Discussion Paper Serie B, University of Bonn, Germany 390, University of Bonn, Germany.
- 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.
- 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.
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