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Axioms for Constant Function Market Makers.

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Τίτλος: Axioms for Constant Function Market Makers.
Συγγραφείς: Schlegel, Christoph1 (AUTHOR) christoph@flashbots.net, Kwaśnicki, Mateusz2 (AUTHOR), Mamageishvili, Akaki3 (AUTHOR)
Πηγή: Mathematical Finance. Jun2026, p1. 17p. 4 Illustrations.
Θεματικοί όροι: *Market makers, *Prediction markets, *Cryptocurrencies, Scale invariance (Statistical physics), Mathematical symmetry, Mathematical logic
Περίληψη: ABSTRACT We study axiomatic foundations for different classes of automated market makers (AMMs). Our main results are a characterization of a generalization of constant product market makers (CPMMs), popular in decentralized finance, and a characterization of the Logarithmic Market Scoring Rule AMM, popular in prediction markets. The first class is characterized by the combination of independence and scale invariance, whereas the second is characterized by the combination of independence and translation invariance. The two classes are, therefore, distinguished by a different invariance property that is motivated by different interpretations of the numéraire in the two applications, but pinned down by the same separability property. Moreover, we characterize the CPMM as trader‐optimal among scale invariant, independent, symmetric and sufficiently funded AMMs. Our results add to a formal analysis of mechanisms used in practice and connect the most popular class of decentralized finance (DeFi) AMMs to the most popular class of prediction market AMMs. [ABSTRACT FROM AUTHOR]
Copyright of Mathematical Finance is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: ABSTRACT We study axiomatic foundations for different classes of automated market makers (AMMs). Our main results are a characterization of a generalization of constant product market makers (CPMMs), popular in decentralized finance, and a characterization of the Logarithmic Market Scoring Rule AMM, popular in prediction markets. The first class is characterized by the combination of independence and scale invariance, whereas the second is characterized by the combination of independence and translation invariance. The two classes are, therefore, distinguished by a different invariance property that is motivated by different interpretations of the numéraire in the two applications, but pinned down by the same separability property. Moreover, we characterize the CPMM as trader‐optimal among scale invariant, independent, symmetric and sufficiently funded AMMs. Our results add to a formal analysis of mechanisms used in practice and connect the most popular class of decentralized finance (DeFi) AMMs to the most popular class of prediction market AMMs. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Mathematical Finance is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Type: doi
        Value: 10.1111/mafi.70041
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 17
        StartPage: 1
    Subjects:
      – SubjectFull: Market makers
        Type: general
      – SubjectFull: Prediction markets
        Type: general
      – SubjectFull: Cryptocurrencies
        Type: general
      – SubjectFull: Scale invariance (Statistical physics)
        Type: general
      – SubjectFull: Mathematical symmetry
        Type: general
      – SubjectFull: Mathematical logic
        Type: general
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      – TitleFull: Axioms for Constant Function Market Makers.
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            NameFull: Kwaśnicki, Mateusz
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            – D: 25
              M: 06
              Text: Jun2026
              Type: published
              Y: 2026
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