Axioms for Constant Function Market Makers

37 Pages Posted: 22 Dec 2022 Last revised: 21 Feb 2023

See all articles by Jan Christoph Schlegel

Jan Christoph Schlegel

City University London

Mateusz Kwaśnicki

Wroclaw University of Science and Technology

Akaki Mamageishvili

Offchain Labs

Date Written: November 30, 2022

Abstract

We study axiomatic foundations for different classes of constant-function automated market makers (CFMMs). We focus particularly on separability and on different invariance properties under scaling. Our main results are an axiomatic characterization of a natural generalization of constant product market makers (CPMMs), popular in decentralized finance, on the one hand, and a characterization of the Logarithmic Scoring Rule Market Makers (LMSR), popular in prediction markets, on the other hand. 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.
However, both are pinned down by the same separability property.
Moreover, we characterize the CPMM as an extremal point within the class of scale invariant, independent, symmetric AMMs with non-concentrated liquidity provision. Our results add to a formal analysis of mechanisms that are currently used for decentralized exchanges and connect the most popular class of DeFi AMMs to the most popular class of prediction market AMMs.

Keywords: Automated Market Maker, Market Microstructure, Decentralized Finance, Blockchain

JEL Classification: D47, D44, D53, G10

Suggested Citation

Schlegel, Jan Christoph and Kwaśnicki, Mateusz and Mamageishvili, Akaki, Axioms for Constant Function Market Makers (November 30, 2022). Available at SSRN: https://ssrn.com/abstract=4290001 or http://dx.doi.org/10.2139/ssrn.4290001

Jan Christoph Schlegel (Contact Author)

City University London ( email )

Northampton Square
London, EC1V 0HB
United Kingdom

Mateusz Kwaśnicki

Wroclaw University of Science and Technology

Akaki Mamageishvili

Offchain Labs ( email )

Zurich
Switzerland

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