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DOI: 10.4230/LIPIcs.AFT.2024.18

Loss-Versus-Fair: Efficiency of Dutch Auctions on Blockchains

Authors: Ciamac C. Moallemi and Dan Robinson

Published in: LIPIcs, Volume 316, 6th Conference on Advances in Financial Technologies (AFT 2024)

Abstract

Milionis et al. (2023) studied the rate at which automated market makers leak value to arbitrageurs when block times are discrete and follow a Poisson process, and where the risky asset price follows a geometric Brownian motion. We extend their model to analyze another popular mechanism in decentralized finance for onchain trading: Dutch auctions. We compute the expected losses that a seller incurs to arbitrageurs and expected time-to-fill for Dutch auctions as a function of starting price, volatility, decay rate, and average interblock time. We also extend the analysis to gradual Dutch auctions, a variation on Dutch auctions for selling tokens over time at a continuous rate. We use these models to explore the tradeoff between speed of execution and quality of execution, which could help inform practitioners in setting parameters for starting price and decay rate on Dutch auctions, or help platform designers determine performance parameters like block times.

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Ciamac C. Moallemi and Dan Robinson. Loss-Versus-Fair: Efficiency of Dutch Auctions on Blockchains. In 6th Conference on Advances in Financial Technologies (AFT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 316, pp. 18:1-18:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{moallemi_et_al:LIPIcs.AFT.2024.18,
  author =	{Moallemi, Ciamac C. and Robinson, Dan},
  title =	{{Loss-Versus-Fair: Efficiency of Dutch Auctions on Blockchains}},
  booktitle =	{6th Conference on Advances in Financial Technologies (AFT 2024)},
  pages =	{18:1--18:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-345-4},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{316},
  editor =	{B\"{o}hme, Rainer and Kiffer, Lucianna},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AFT.2024.18},
  URN =		{urn:nbn:de:0030-drops-209541},
  doi =		{10.4230/LIPIcs.AFT.2024.18},
  annote =	{Keywords: Dutch auctions, blockchain, decentralized finance}
}

Document

DOI: 10.4230/LIPIcs.ITCS.2024.81

A Myersonian Framework for Optimal Liquidity Provision in Automated Market Makers

Authors: Jason Milionis, Ciamac C. Moallemi, and Tim Roughgarden

Published in: LIPIcs, Volume 287, 15th Innovations in Theoretical Computer Science Conference (ITCS 2024)

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.

Cite as

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)

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@InProceedings{milionis_et_al:LIPIcs.ITCS.2024.81,
  author =	{Milionis, Jason and Moallemi, Ciamac C. and Roughgarden, Tim},
  title =	{{A Myersonian Framework for Optimal Liquidity Provision in Automated Market Makers}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{81:1--81:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-309-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{287},
  editor =	{Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.81},
  URN =		{urn:nbn:de:0030-drops-196094},
  doi =		{10.4230/LIPIcs.ITCS.2024.81},
  annote =	{Keywords: Posted-Price Mechanisms, Asset Exchange, Market Making, Automated Market Makers (AMMs), Blockchains, Decentralized Finance, Incentive Compatibility, Optimization}
}

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Documents authored by Moallemi, Ciamac C.

Loss-Versus-Fair: Efficiency of Dutch Auctions on Blockchains

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A Myersonian Framework for Optimal Liquidity Provision in Automated Market Makers

Abstract

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