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A Myersonian Framework for Optimal Liquidity Provision in Automated Market Makers

Authors Jason Milionis , Ciamac C. Moallemi , Tim Roughgarden

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Author Details

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

Funding

  • Milionis, Jason: Supported in part by NSF awards CNS-2212745, CCF-2212233, DMS-2134059, and CCF-1763970.
  • Moallemi, Ciamac C.: Supported by the Briger Family Digital Finance Lab at Columbia Business School.
  • Roughgarden, Tim: Research at Columbia University supported in part by NSF awards CNS-2212745, and CCF-2006737.

Cite AsGet BibTex

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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