A truthful two-stage mechanism for eliciting probabilistic estimates with unknown costs

Athanasios Papakonstantinou, Alex Rogers, Enrico H. Gerding, Nicholas R. Jennings

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Abstract

This 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.
Original languageEnglish
Title of host publicationECAI 2008 Proceedings
EditorsMalik Ghallab, Constantine D. Spyropoulos, Nikos Fakotakis, Nikolaos M. Avouris
Publication date2008
Pages448 - 452
ISBN (Print)978-1-58603-891-5
Publication statusPublished - 2008
Externally publishedYes
Event18th European Conference on Artificial Intelligence - Patras, Greece
Duration: 21 Jul 200825 Jul 2008

Conference

Conference18th European Conference on Artificial Intelligence
CountryGreece
CityPatras
Period21/07/200825/07/2008
SeriesFrontiers in Artificial Intelligence and Applications
Volume178
ISSN0922-6389

Bibliographical note

http://ebooks.iospress.nl/volumearticle/4410

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