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DOI: 10.4230/LIPIcs.ITCS.2024.51

An Axiomatic Characterization of CFMMs and Equivalence to Prediction Markets

Authors: Rafael Frongillo, Maneesha Papireddygari, and Bo Waggoner

Published in: LIPIcs, Volume 287, 15th Innovations in Theoretical Computer Science Conference (ITCS 2024)

Abstract

Constant-function market makers (CFMMs), such as Uniswap, are automated exchanges offering trades among a set of assets. We study their technical relationship to another class of automated market makers, cost-function prediction markets. We first introduce axioms for market makers and show that CFMMs with concave potential functions characterize "good" market makers according to these axioms. We then show that every such CFMM on n assets is equivalent to a cost-function prediction market for events with n outcomes. Our construction directly converts a CFMM into a prediction market, and vice versa. Using this equivalence, we give another construction which can produce any 1-homogenous, increasing, and concave CFMM, as are typically used in practice, from a cost function. Conceptually, our results show that desirable market-making axioms are equivalent to desirable information-elicitation axioms, i.e., markets are good at facilitating trade if and only if they are good at revealing beliefs. For example, we show that every CFMM implicitly defines a proper scoring rule for eliciting beliefs; the scoring rule for Uniswap is unusual, but known. From a technical standpoint, our results show how tools for prediction markets and CFMMs can interoperate. We illustrate this interoperability by showing how liquidity strategies from both literatures transfer to the other, yielding new market designs.

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Rafael Frongillo, Maneesha Papireddygari, and Bo Waggoner. An Axiomatic Characterization of CFMMs and Equivalence to Prediction Markets. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 51:1-51:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{frongillo_et_al:LIPIcs.ITCS.2024.51,
  author =	{Frongillo, Rafael and Papireddygari, Maneesha and Waggoner, Bo},
  title =	{{An Axiomatic Characterization of CFMMs and Equivalence to Prediction Markets}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{51:1--51:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-309-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{287},
  editor =	{Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.51},
  URN =		{urn:nbn:de:0030-drops-195795},
  doi =		{10.4230/LIPIcs.ITCS.2024.51},
  annote =	{Keywords: Convex analysis, Equivalence result, Axiomatic characterization, Market Makers, Prediction markets, Scoring rules, Cost-functions}
}

Document

DOI: 10.4230/LIPIcs.ITCS.2018.15

An Axiomatic Study of Scoring Rule Markets

Authors: Rafael Frongillo and Bo Waggoner

Published in: LIPIcs, Volume 94, 9th Innovations in Theoretical Computer Science Conference (ITCS 2018)

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.

Cite as

Rafael Frongillo and Bo Waggoner. An Axiomatic Study of Scoring Rule Markets. In 9th Innovations in Theoretical Computer Science Conference (ITCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 94, pp. 15:1-15:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{frongillo_et_al:LIPIcs.ITCS.2018.15,
  author =	{Frongillo, Rafael and Waggoner, Bo},
  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 =	{Karlin, Anna R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2018.15},
  URN =		{urn:nbn:de:0030-drops-83611},
  doi =		{10.4230/LIPIcs.ITCS.2018.15},
  annote =	{Keywords: prediction markets, information elicitation, scoring rules}
}

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An Axiomatic Characterization of CFMMs and Equivalence to Prediction Markets

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An Axiomatic Study of Scoring Rule Markets

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