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The economics of constant function market makers

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  • Michele Fabi

    (CREST - Centre de Recherche en Economie et Statistique [Bruz] - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - GENES - Groupe des Écoles Nationales d'Économie et Statistique, ECO-Télécom Paris - Equipe Eco Economie - CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - GENES - Groupe des Écoles Nationales d'Économie et Statistique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - GENES - Groupe des Écoles Nationales d'Économie et Statistique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique, SES - Département Sciences Economiques et Sociales - Télécom Paris - IMT - Institut Mines-Télécom [Paris] - IP Paris - Institut Polytechnique de Paris)

  • Julien Prat

    (CNRS - Centre National de la Recherche Scientifique, X - École polytechnique - IP Paris - Institut Polytechnique de Paris, CREST - Centre de Recherche en Economie et Statistique [Bruz] - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - GENES - Groupe des Écoles Nationales d'Économie et Statistique, IP Paris - Institut Polytechnique de Paris)

Abstract

We use microeconomic theory to describe the inner workings of Constant Function Market Makers (CFMMs). We show that standard results from consumer theory apply in this new context, endowing us with powerful tools to characterize the optimal design of CFMMs. We employ them to analyze the externalities that traders and liquidity providers exert on each other when interacting through a CFMM. Liquidity providers reduce the execution costs by flattening the bonding curve on which trades are executed.Arbitrageurs impose an adverse selection cost on liquidity providers by unfavorably rebalancing their portfolio. We show that the strengths of these two externalities are pinned down by the curvature of the bonding curve and are inversely related to each other, thereby identifying the fundamental economic tradeoff that market designers have to address.

Suggested Citation

  • Michele Fabi & Julien Prat, 2024. "The economics of constant function market makers," Working Papers hal-04920095, HAL.
    • Handle: RePEc:hal:wpaper:hal-04920095
    DOI: 10.1016/j.jcorpfin.2025.102737
    Note: View the original document on HAL open archive server: https://hal.science/hal-04920095v1
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    JEL classification:

    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design
    • D53 - Microeconomics - - General Equilibrium and Disequilibrium - - - Financial Markets

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