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Towards a Theory of Maximal Extractable Value I: Constant Function Market Makers

Author

Listed:
  • Kshitij Kulkarni
  • Theo Diamandis
  • Tarun Chitra

Abstract

Maximal Extractable Value (MEV) refers to excess value captured by miners (or validators) from users in a cryptocurrency network. This excess value often comes from reordering users' transactions to maximize fees or from inserting new transactions that front-run users' transactions. One of the most common types of MEV involves a `sandwich attack' against a user trading on a constant function market maker (CFMM), which is a popular class of automated market maker. We analyze game theoretic properties of MEV in CFMMs that we call \textit{routing} and \textit{reordering} MEV. In the case of routing, we present examples where the existence of MEV both degrades and, counterintuitively, \emph{improves} the quality of routing. We construct an analogue of the price of anarchy for this setting and demonstrate that if the impact of a sandwich attack is localized in a suitable sense, then the price of anarchy is constant. In the case of reordering, we show conditions when the maximum price impact caused by the reordering of sandwich attacks in a sequence of trades, relative to the average price, impact is $O(\log n)$ in the number of user trades. Combined, our results suggest methods that both MEV searchers and CFMM designers can utilize for estimating costs and profits of MEV.

Suggested Citation

  • Kshitij Kulkarni & Theo Diamandis & Tarun Chitra, 2022. "Towards a Theory of Maximal Extractable Value I: Constant Function Market Makers," Papers 2207.11835, arXiv.org, revised Apr 2023.
    • Handle: RePEc:arx:papers:2207.11835
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    File URL: http://arxiv.org/pdf/2207.11835
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    References listed on IDEAS

    as
    1. Guillermo Angeris & Tarun Chitra, 2020. "Improved Price Oracles: Constant Function Market Makers," Papers 2003.10001, arXiv.org, revised Jun 2020.
    2. Guillermo Angeris & Tarun Chitra & Alex Evans & Stephen Boyd, 2022. "Optimal Routing for Constant Function Market Makers," Papers 2204.05238, arXiv.org.
    3. Saeed Alaei & Ali Makhdoumi & Azarakhsh Malekian & Rad Niazadeh, 2022. "Descending Price Auctions with Bounded Number of Price Levels and Batched Prophet Inequality," Papers 2203.01384, arXiv.org.
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    Cited by:

    1. Elijah Fox & Mallesh Pai & Max Resnick, 2023. "Censorship Resistance in On-Chain Auctions," Papers 2301.13321, arXiv.org, revised Jun 2023.

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