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Constant Function Market Makers: Multi-asset Trades via Convex Optimization

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Handbook on Blockchain

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 194))

Abstract

The rise of Ethereum and other blockchains that support smart contracts has led to the creation of decentralized exchanges (DEXs), such as Uniswap, Balancer, Curve, mStable, and SushiSwap, which enable agents to trade cryptocurrencies without trusting a centralized authority. While traditional exchanges use order books to match and execute trades, DEXs are typically organized as constant function market makers (CFMMs). CFMMs accept and reject proposed trades based on the evaluation of a function that depends on the proposed trade and the current reserves of the DEX. For trades that involve only two assets, CFMMs are easy to understand, via two functions that give the quantity of one asset that must be tendered to receive a given quantity of the other, and vice versa. When more than two assets are being exchanged, it is harder to understand the landscape of possible trades. We observe that various problems of choosing a multi-asset trade can be formulated as convex optimization problems and can therefore be reliably and efficiently solved.

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Acknowledgements

The authors would like to acknowledge Shane Barratt for useful discussions. Guillermo Angeris is supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE-1656518. Akshay Agrawal is supported by a Stanford Graduate Fellowship.

Author information

Authors and Affiliations

  1. Stanford University, Stanford, USA

    Guillermo Angeris, Akshay Agrawal & Stephen Boyd

  2. Bain Capital Crypto, Charlotte, USA

    Alex Evans

  3. Gauntlet Networks, New York, USA

    Tarun Chitra

Authors
  1. Guillermo Angeris
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  2. Akshay Agrawal
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  3. Alex Evans
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  4. Tarun Chitra
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  5. Stephen Boyd
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Corresponding author

Correspondence to Guillermo Angeris .

Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Massachusetts Boston, Boston, MA, USA

    Duc A. Tran

  2. Department of Computer and Information Science and Engineering, University of Florida, Gainesville, FL, USA

    My T. Thai

  3. Department of Electrical and Computer Engineering, University of Southern California, Los Angeles, CA, USA

    Bhaskar Krishnamachari

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Angeris, G., Agrawal, A., Evans, A., Chitra, T., Boyd, S. (2022). Constant Function Market Makers: Multi-asset Trades via Convex Optimization. In: Tran, D.A., Thai, M.T., Krishnamachari, B. (eds) Handbook on Blockchain. Springer Optimization and Its Applications, vol 194. Springer, Cham. https://doi.org/10.1007/978-3-031-07535-3_13

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