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Automated Market Makers for Decentralized Finance (DeFi)

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  • Yongge Wang

Abstract

This paper compares mathematical models for automated market makers including logarithmic market scoring rule (LMSR), liquidity sensitive LMSR (LS-LMSR), constant product/mean/sum, and others. It is shown that though LMSR may not be a good model for Decentralized Finance (DeFi) applications, LS-LMSR has several advantages over constant product/mean based automated market makers. However, LS-LMSR requires complicated computation (i.e., logarithm and exponentiation) and the cost function curve is concave. In certain DeFi applications, it is preferred to have computationally efficient cost functions with convex curves to conform with the principle of supply and demand. This paper proposes and analyzes constant circle/ellipse based cost functions for automated market makers. The proposed cost functions are computationally efficient (only requires multiplication and square root calculation) and have several advantages over widely deployed constant product cost functions. For example, the proposed market makers are more robust against front-runner (slippage) attacks.

Suggested Citation

  • Yongge Wang, 2020. "Automated Market Makers for Decentralized Finance (DeFi)," Papers 2009.01676, arXiv.org, revised Sep 2020.
    • Handle: RePEc:arx:papers:2009.01676
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    File URL: http://arxiv.org/pdf/2009.01676
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    References listed on IDEAS

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    1. Robin Hanson, 2007. "Logarithmic Market Scoring Rules for Modular Combinatorial Information Aggregation," Journal of Prediction Markets, University of Buckingham Press, vol. 1(1), pages 3-15, February.
    2. Fama, Eugene F, 1970. "Efficient Capital Markets: A Review of Theory and Empirical Work," Journal of Finance, American Finance Association, vol. 25(2), pages 383-417, May.
    3. Robin Hanson, 2003. "Combinatorial Information Market Design," Information Systems Frontiers, Springer, vol. 5(1), pages 107-119, January.
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    Cited by:

    1. Arman Abgaryan & Utkarsh Sharma, 2023. "Dynamic Function Market Maker," Papers 2307.13624, arXiv.org.
    2. Massimo Bartoletti & James Hsin-yu Chiang & Alberto Lluch-Lafuente, 2020. "SoK: Lending Pools in Decentralized Finance," Papers 2012.13230, arXiv.org.
    3. Daniel Kirste & Niclas Kannengie{ss}er & Ricky Lamberty & Ali Sunyaev, 2023. "How Automated Market Makers Approach the Thin Market Problem in Cryptoeconomic Systems," Papers 2309.12818, arXiv.org, revised Sep 2023.
    4. Bhaskar Krishnamachari & Qi Feng & Eugenio Grippo, 2021. "Dynamic Curves for Decentralized Autonomous Cryptocurrency Exchanges," Papers 2101.02778, arXiv.org.
    5. Dev Churiwala & Bhaskar Krishnamachari, 2022. "QLAMMP: A Q-Learning Agent for Optimizing Fees on Automated Market Making Protocols," Papers 2211.14977, arXiv.org.

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