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Automated Market Making and Arbitrage Profits in the Presence of Fees

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  • Jason Milionis
  • Ciamac C. Moallemi
  • Tim Roughgarden

Abstract

We consider the impact of trading fees on the profits of arbitrageurs trading against an automated marker marker (AMM) or, equivalently, on the adverse selection incurred by liquidity providers due to arbitrage. We extend the model of Milionis et al. [2022] for a general class of two asset AMMs to both introduce fees and discrete Poisson block generation times. In our setting, we are able to compute the expected instantaneous rate of arbitrage profit in closed form. When the fees are low, in the fast block asymptotic regime, the impact of fees takes a particularly simple form: fees simply scale down arbitrage profits by the fraction of time that an arriving arbitrageur finds a profitable trade.

Suggested Citation

  • Jason Milionis & Ciamac C. Moallemi & Tim Roughgarden, 2023. "Automated Market Making and Arbitrage Profits in the Presence of Fees," Papers 2305.14604, arXiv.org.
    • Handle: RePEc:arx:papers:2305.14604
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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.
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    Cited by:

    1. 'Alvaro Cartea & Fayc{c}al Drissi & Marcello Monga, 2023. "Decentralised Finance and Automated Market Making: Predictable Loss and Optimal Liquidity Provision," Papers 2309.08431, arXiv.org, revised Jun 2024.
    2. Andrea Canidio & Robin Fritsch, 2023. "Arbitrageurs' profits, LVR, and sandwich attacks: batch trading as an AMM design response," Papers 2307.02074, arXiv.org, revised Feb 2024.
    3. Pablo D. Azar & Adrian Casillas & Maryam Farboodi, 2024. "Information and Market Power in DeFi Intermediation," Staff Reports 1102, Federal Reserve Bank of New York.
    4. Lioba Heimbach & Vabuk Pahari & Eric Schertenleib, 2024. "Non-Atomic Arbitrage in Decentralized Finance," Papers 2401.01622, arXiv.org, revised Apr 2024.
    5. Joseph Najnudel & Shen-Ning Tung & Kazutoshi Yamazaki & Ju-Yi Yen, 2024. "An arbitrage driven price dynamics of Automated Market Makers in the presence of fees," Papers 2401.01526, arXiv.org.
    6. Austin Adams & Benjamin Y Chan & Sarit Markovich & Xin Wan, 2023. "Don't Let MEV Slip: The Costs of Swapping on the Uniswap Protocol," Papers 2309.13648, arXiv.org, revised Apr 2024.
    7. Cheuk Yin Lee & Shen-Ning Tung & Tai-Ho Wang, 2024. "Growth rate of liquidity provider's wealth in G3Ms," Papers 2403.18177, arXiv.org.
    8. Viraj Nadkarni & Sanjeev Kulkarni & Pramod Viswanath, 2024. "Adaptive Curves for Optimally Efficient Market Making," Papers 2406.13794, arXiv.org.
    9. Ciamac C. Moallemi & Dan Robinson, 2024. "Loss-Versus-Fair: Efficiency of Dutch Auctions on Blockchains," Papers 2406.00113, arXiv.org, revised Jul 2024.
    10. Marcello Monga, 2024. "Automated Market Making and Decentralized Finance," Papers 2407.16885, arXiv.org.

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