License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ITCS.2018.15
URN: urn:nbn:de:0030-drops-83611
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/8361/
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Frongillo, Rafael ; Waggoner, Bo

An Axiomatic Study of Scoring Rule Markets

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LIPIcs-ITCS-2018-15.pdf (0.8 MB)

Abstract

Prediction markets are well-studied in the case where predictions are probabilities or expectations of future random variables. In 2008, Lambert, et al. proposed a generalization, which we call "scoring rule markets" (SRMs), in which traders predict the value of arbitrary statistics of the random variables, provided these statistics can be elicited by a scoring rule. Surprisingly, despite active recent work on prediction markets, there has not yet been any investigation into more general SRMs. To initiate such a study, we ask the following question: in what sense are SRMs "markets"? We classify SRMs according to several axioms that capture potentially desirable qualities of a market, such as the ability to freely exchange goods (contracts) for money. Not all SRMs satisfy our axioms: once a contract is purchased in any market for prediction the median of some variable, there will not necessarily be any way to sell that contract back, even in a very weak sense. Our main result is a characterization showing that slight generalizations of cost-function-based markets are the only markets to satisfy all of our axioms for finite-outcome random variables. Nonetheless, we find that several SRMs satisfy weaker versions of our axioms, including a novel share-based market mechanism for ratios of expected values.

BibTeX - Entry

@InProceedings{frongillo_et_al:LIPIcs:2018:8361,
  author =	{Rafael Frongillo and Bo Waggoner},
  title =	{{An Axiomatic Study of Scoring Rule Markets}},
  booktitle =	{9th Innovations in Theoretical Computer Science Conference (ITCS 2018)},
  pages =	{15:1--15:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-060-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{94},
  editor =	{Anna R. Karlin},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/8361},
  URN =		{urn:nbn:de:0030-drops-83611},
  doi =		{10.4230/LIPIcs.ITCS.2018.15},
  annote =	{Keywords: prediction markets, information elicitation, scoring rules}
}

Keywords: prediction markets, information elicitation, scoring rules
Collection: 9th Innovations in Theoretical Computer Science Conference (ITCS 2018)
Issue Date: 2018
Date of publication: 12.01.2018

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