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G3Ms:Generalized Mean Market Makers

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  • Daniel Z. Zanger

Abstract

In the Decentralized Finance (DeFi) setting, we present a new parametrized family of Constant Function Market Makers (CFMMs) which we call the Generalized Mean Market Makers (G3Ms), based on the generalized means. The G3Ms are intermediate between the Arithmetic Mean and Geometric Mean CFMM models, which G3Ms incorporate as special cases. We also present an extension of the G3Ms, based on the so-called Generalized f-Means, called Generalized f-Mean Market Makers (Gf3Ms). We show in addition that the G3Ms possess certain properties preferable to those exhibited by either the Arithmetic Mean CFMM or the Geometric Mean CFMM alone.

Suggested Citation

  • Daniel Z. Zanger, 2022. "G3Ms:Generalized Mean Market Makers," Papers 2208.07305, arXiv.org.
    • Handle: RePEc:arx:papers:2208.07305
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    References listed on IDEAS

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    1. Guillermo Angeris & Tarun Chitra, 2020. "Improved Price Oracles: Constant Function Market Makers," Papers 2003.10001, arXiv.org, revised Jun 2020.
    2. Bhaskar Krishnamachari & Qi Feng & Eugenio Grippo, 2021. "Dynamic Curves for Decentralized Autonomous Cryptocurrency Exchanges," Papers 2101.02778, arXiv.org.
    3. Guillermo Angeris & Akshay Agrawal & Alex Evans & Tarun Chitra & Stephen Boyd, 2021. "Constant Function Market Makers: Multi-Asset Trades via Convex Optimization," Papers 2107.12484, arXiv.org.
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    Cited by:

    1. Xue Dong He & Chen Yang & Yutian Zhou, 2024. "Optimal Design of Automated Market Makers on Decentralized Exchanges," Papers 2404.13291, arXiv.org, revised Nov 2024.

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