{"title":"DEX Specs: A Mean Field Approach to DeFi Currency Exchanges","authors":"Erhan Bayraktar, Asaf Cohen, April Nellis","doi":"arxiv-2404.09090","DOIUrl":null,"url":null,"abstract":"We investigate the behavior of liquidity providers (LPs) by modeling a\ndecentralized cryptocurrency exchange (DEX) based on Uniswap v3. LPs with\nheterogeneous characteristics choose optimal liquidity positions subject to\nuncertainty regarding the size of exogenous incoming transactions and the\nprices of assets in the wider market. They engage in a game among themselves,\nand the resulting liquidity distribution determines the exchange rate dynamics\nand potential arbitrage opportunities of the pool. We calibrate the\ndistribution of LP characteristics based on Uniswap data and the equilibrium\nstrategy resulting from this mean-field game produces pool exchange rate\ndynamics and liquidity evolution consistent with observed pool behavior. We\nsubsequently introduce Maximal Extractable Value (MEV) bots who perform\nJust-In-Time (JIT) liquidity attacks, and develop a Stackelberg game between\nLPs and bots. This addition results in more accurate simulated pool exchange\nrate dynamics and stronger predictive power regarding the evolution of the pool\nliquidity distribution.","PeriodicalId":501478,"journal":{"name":"arXiv - QuantFin - Trading and Market Microstructure","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - QuantFin - Trading and Market Microstructure","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2404.09090","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We investigate the behavior of liquidity providers (LPs) by modeling a
decentralized cryptocurrency exchange (DEX) based on Uniswap v3. LPs with
heterogeneous characteristics choose optimal liquidity positions subject to
uncertainty regarding the size of exogenous incoming transactions and the
prices of assets in the wider market. They engage in a game among themselves,
and the resulting liquidity distribution determines the exchange rate dynamics
and potential arbitrage opportunities of the pool. We calibrate the
distribution of LP characteristics based on Uniswap data and the equilibrium
strategy resulting from this mean-field game produces pool exchange rate
dynamics and liquidity evolution consistent with observed pool behavior. We
subsequently introduce Maximal Extractable Value (MEV) bots who perform
Just-In-Time (JIT) liquidity attacks, and develop a Stackelberg game between
LPs and bots. This addition results in more accurate simulated pool exchange
rate dynamics and stronger predictive power regarding the evolution of the pool
liquidity distribution.
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