A Myersonian Framework for Optimal Liquidity Provision in Automated Market Makers

Authors Jason Milionis , Ciamac C. Moallemi , Tim Roughgarden



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Jason Milionis
  • Department of Computer Science, Columbia University, New York, NY, USA
Ciamac C. Moallemi
  • Graduate School of Business, Columbia University, New York, NY, USA
Tim Roughgarden
  • Department of Computer Science, Columbia University, New York, NY, USA
  • a16z Crypto, New York NY 10010, USA

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Jason Milionis, Ciamac C. Moallemi, and Tim Roughgarden. A Myersonian Framework for Optimal Liquidity Provision in Automated Market Makers. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 81:1-81:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.ITCS.2024.81

Abstract

In decentralized finance ("DeFi"), automated market makers (AMMs) enable traders to programmatically exchange one asset for another. Such trades are enabled by the assets deposited by liquidity providers (LPs). The goal of this paper is to characterize and interpret the optimal (i.e., profit-maximizing) strategy of a monopolist liquidity provider, as a function of that LP’s beliefs about asset prices and trader behavior. We introduce a general framework for reasoning about AMMs based on a Bayesian-like belief inference framework, where LPs maintain an asset price estimate, which is updated by incorporating traders' price estimates. In this model, the market maker (i.e., LP) chooses a demand curve that specifies the quantity of a risky asset to be held at each dollar price. Traders arrive sequentially and submit a price bid that can be interpreted as their estimate of the risky asset price; the AMM responds to this submitted bid with an allocation of the risky asset to the trader, a payment that the trader must pay, and a revised internal estimate for the true asset price. We define an incentive-compatible (IC) AMM as one in which a trader’s optimal strategy is to submit its true estimate of the asset price, and characterize the IC AMMs as those with downward-sloping demand curves and payments defined by a formula familiar from Myerson’s optimal auction theory. We generalize Myerson’s virtual values, and characterize the profit-maximizing IC AMM. The optimal demand curve generally has a jump that can be interpreted as a "bid-ask spread," which we show is caused by a combination of adverse selection risk (dominant when the degree of information asymmetry is large) and monopoly pricing (dominant when asymmetry is small). This work opens up new research directions into the study of automated exchange mechanisms from the lens of optimal auction theory and iterative belief inference, using tools of theoretical computer science in a novel way.

Subject Classification

ACM Subject Classification
  • Theory of computation → Algorithmic game theory
  • Theory of computation → Algorithmic mechanism design
  • Theory of computation → Computational pricing and auctions
Keywords
  • Posted-Price Mechanisms
  • Asset Exchange
  • Market Making
  • Automated Market Makers (AMMs)
  • Blockchains
  • Decentralized Finance
  • Incentive Compatibility
  • Optimization

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References

  1. Jacob Abernethy and Satyen Kale. Adaptive market making via online learning. In C.J. Burges, L. Bottou, M. Welling, Z. Ghahramani, and K.Q. Weinberger, editors, Advances in Neural Information Processing Systems, volume 26. Curran Associates, Inc., 2013. URL: https://proceedings.neurips.cc/paper_files/paper/2013/file/995e1fda4a2b5f55ef0df50868bf2a8f-Paper.pdf.
  2. Saeed Alaei, Hu Fu, Nima Haghpanah, and Jason Hartline. The simple economics of approximately optimal auctions. In 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, pages 628-637. IEEE, 2013. Google Scholar
  3. Guillermo Angeris and Tarun Chitra. Improved price oracles: Constant function market makers. In Proceedings of the 2nd ACM Conference on Advances in Financial Technologies, pages 80-91, 2020. Google Scholar
  4. Guillermo Angeris, Alex Evans, and Tarun Chitra. Replicating market makers. arXiv preprint, 2021. URL: https://arxiv.org/abs/2103.14769.
  5. Guillermo Angeris, Alex Evans, and Tarun Chitra. Replicating monotonic payoffs without oracles. arXiv preprint, 2021. URL: https://arxiv.org/abs/2111.13740.
  6. Aseem Brahma, Mithun Chakraborty, Sanmay Das, Allen Lavoie, and Malik Magdon-Ismail. A bayesian market maker. In Proceedings of the 13th ACM Conference on Electronic Commerce, EC '12, pages 215-232, New York, NY, USA, 2012. Association for Computing Machinery. URL: https://doi.org/10.1145/2229012.2229031.
  7. Jeremy Bulow and John Roberts. The simple economics of optimal auctions. Journal of Political Economy, 97(5):1060-1090, 1989. URL: https://doi.org/10.1086/261643.
  8. Shuchi Chawla, Jason D Hartline, and Robert Kleinberg. Algorithmic pricing via virtual valuations. In Proceedings of the 8th ACM Conference on Electronic Commerce, pages 243-251, 2007. Google Scholar
  9. Shuchi Chawla, Jason D Hartline, David L Malec, and Balasubramanian Sivan. Multi-parameter mechanism design and sequential posted pricing. In Proceedings of the forty-second ACM symposium on Theory of computing, pages 311-320, 2010. Google Scholar
  10. Shuchi Chawla, Jason D Hartline, and Balasubramanian Sivan. Optimal crowdsourcing contests. Games and Economic Behavior, 113:80-96, 2019. URL: https://doi.org/10.1016/j.geb.2015.09.001.
  11. Y. Chen and D.M Pennock. A utility framework for bounded-loss market makers. In Proceedings of the 23rd Conference on Uncertainty in Artificial Intelligence (UAI 2007, pages 49-56, Vancouver, BC, Canada, 2007. Google Scholar
  12. Richard Cole and Shravas Rao. Applications of α-strongly regular distributions to bayesian auctions. ACM Trans. Econ. Comput., 5(4), December 2017. URL: https://doi.org/10.1145/3157083.
  13. Richard Cole and Tim Roughgarden. The sample complexity of revenue maximization. In Proceedings of the forty-sixth annual ACM symposium on Theory of computing, pages 243-252, 2014. Google Scholar
  14. Sanmay Das. A learning market-maker in the glosten-milgrom model. Quantitative Finance, 5(2):169-180, 2005. Google Scholar
  15. Sanmay Das and Malik Magdon-Ismail. Adapting to a market shock: Optimal sequential market-making. In D. Koller, D. Schuurmans, Y. Bengio, and L. Bottou, editors, Advances in Neural Information Processing Systems, volume 21. Curran Associates, Inc., 2008. URL: https://proceedings.neurips.cc/paper_files/paper/2008/file/7a614fd06c325499f1680b9896beedeb-Paper.pdf.
  16. Christian Ewerhart. Regular type distributions in mechanism design and ρ-concavity. Economic Theory, 53(3):591-603, 2013. The original publication is available at www.springerlink.com. URL: https://doi.org/10.1007/s00199-012-0705-3.
  17. Zhou Fan, Francisco J. Marmolejo-Cossío, Ben Altschuler, He Sun, Xintong Wang, and David Parkes. Differential liquidity provision in uniswap v3 and implications for contract design. In Proceedings of the Third ACM International Conference on AI in Finance, ICAIF '22, pages 9-17, New York, NY, USA, 2022. Association for Computing Machinery. URL: https://doi.org/10.1145/3533271.3561775.
  18. Andrew Gelman, John B. Carlin, Hal Steven Stern, David B. Dunson, Aki Vehtari, and Donald B. Rubin. Bayesian data analysis. CRC Press, Boca Raton, third edition edition, 2014. OCLC: 909477393. Google Scholar
  19. Lawrence R Glosten. Insider trading, liquidity, and the role of the monopolist specialist. Journal of business, pages 211-235, 1989. Google Scholar
  20. Lawrence R Glosten. Is the electronic open limit order book inevitable? The Journal of Finance, 49(4):1127-1161, 1994. Google Scholar
  21. Lawrence R. Glosten and Paul R. Milgrom. Bid, ask and transaction prices in a specialist market with heterogeneously informed traders. Journal of Financial Economics, 14(1):71-100, 1985. URL: https://doi.org/10.1016/0304-405X(85)90044-3.
  22. Mohak Goyal, Geoffrey Ramseyer, Ashish Goel, and David Mazières. Finding the right curve: Optimal design of constant function market makers, 2022. URL: https://doi.org/10.48550/arXiv.2212.03340.
  23. Nima Haghpanah and Jason D Hartline. Reverse mechanism design. In Proceedings of the Sixteenth ACM Conference on Economics and Computation, pages 757-758, 2015. Google Scholar
  24. Jason D Hartline. Approximation in mechanism design. American Economic Review, 102(3):330-336, 2012. Google Scholar
  25. Jason D Hartline. Mechanism design and approximation. Book draft, 122(1), 2021. Google Scholar
  26. Jason D Hartline and Tim Roughgarden. Simple versus optimal mechanisms. In Proceedings of the 10th ACM conference on Electronic commerce, pages 225-234, 2009. Google Scholar
  27. Albert S. Kyle. Continuous auctions and insider trading. Econometrica, 53(6):1315-1335, 1985. URL: http://www.jstor.org/stable/1913210.
  28. Albert S. Kyle. Informed speculation with imperfect competition. The Review of Economic Studies, 56(3):317-355, 1989. URL: http://www.jstor.org/stable/2297551.
  29. Nathan Mantel. Tails of distributions. The American Statistician, 30(1):14-17, 1976. URL: http://www.jstor.org/stable/2682880.
  30. Jason Milionis, Ciamac C. Moallemi, and Tim Roughgarden. Complexity-Approximation Trade-offs in Exchange Mechanisms: AMMs vs. LOBs. In Financial Cryptography and Data Security. Springer International Publishing, 2023. Google Scholar
  31. Jason Milionis, Ciamac C. Moallemi, and Tim Roughgarden. Extended Abstract: The Effect of Trading Fees on Arbitrage Profits in Automated Market Makers. In Financial Cryptography and Data Security. FC 2023 International Workshops. Springer International Publishing, 2023. Google Scholar
  32. Jason Milionis, Ciamac C. Moallemi, Tim Roughgarden, and Anthony Lee Zhang. Quantifying loss in automated market makers. In Proceedings of the 2022 ACM CCS Workshop on Decentralized Finance and Security, DeFi'22, pages 71-74, New York, NY, USA, 2022. Association for Computing Machinery. URL: https://doi.org/10.1145/3560832.3563441.
  33. Roger B. Myerson. Optimal auction design. Mathematics of Operations Research, 6(1):58-73, 1981. URL: http://www.jstor.org/stable/3689266.
  34. Michael Neuder, Rithvik Rao, Daniel J Moroz, and David C Parkes. Strategic liquidity provision in uniswap v3. arXiv preprint, 2021. URL: https://arxiv.org/abs/2106.12033.
  35. Maureen O'Hara. Market microstructure theory. Blackwell, Malden, Mass., repr. edition, 2011. Google Scholar
  36. Tim Roughgarden and Inbal Talgam-Cohen. Optimal and robust mechanism design with interdependent values. ACM Transactions on Economics and Computation (TEAC), 4(3):1-34, 2016. Google Scholar
  37. Tim Roughgarden and Inbal Talgam-Cohen. Approximately optimal mechanism design. Annual Review of Economics, 11:355-381, 2019. Google Scholar
  38. Jimmy Yin and Mac Ren. On liquidity mining for uniswap v3. arXiv preprint, 2021. URL: https://arxiv.org/abs/2108.05800.