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DEX Specs: A Mean Field Approach to DeFi Currency Exchanges
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DEX Specs: A Mean Field Approach to DeFi Currency Exchanges
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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.
Forward citations
Cited by 3 Pith papers
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Liquidity provision in CLMMs: evidence from transactions data
Only about one in six liquidity providers in WETH/USD pools on Base avoid losses; profitable positions concentrate near the current price and are closed before the full range is crossed.
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Causal Effects of Protocol-Fee Changes on Liquidity Provision in Automated Market Makers
A matched-overlap event-study DiD of Uniswap’s protocol-fee switch finds no large short-run average LP liquidity, depth, or participation response to take-rate cuts.
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A New Framework for Modelling Liquidity Pools as Mean Field Games
Develops a mean field game framework for liquidity pools in constant-product AMMs, proving existence of solutions and approximate Nash equilibria while validating via numerical simulations of stability and convergence.
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