April Nellis

Job Market Paper Abstract:

We study and model the behavior of liquidity providers in a decentralized cryptocurrency exchange (DEX). Players choose an optimal liquidity position subject to uncertainty regarding the size of exogenous incoming trader transactions and the relative price of the assets in a wider, “infinite-liquidity” market. Liquidity providers engage in a game among themselves, and the resulting liquidity distribution determines the price dynamics and potential arbitrage opportunities of the pool. We emulate the Uniswap v3 Constant Product Market Maker (CPMM) exchange function with concentrated liquidity. In our model, the equilibrium strategy of the mean-field game (MFG) results in a pool exchange rate that closely follows the market exchange rate, which is consistent with real-world data. In addition, we find that we are able to recreate a scenario in which the equilibrium mean field is also consistent with observed liquidity distribution data. We subsequently introduce MEV bot attackers and develop a Stackelberg game between liquidity providers and bots. The anticipations of bots results in a different equilibrium strategy for liquidity providers, and we discuss the benefits and costs of such a strategy.

For full working paper, feel free to email me at nellisa (at) umich (dot) edu

About Me:

Hi there! I'm a current Ph.D. student in the Applied and Interdisciplinary Mathematics program at University of Michigan. 

I graduated from University of Maryland, College Park in 2019 with joint degrees in Applied Mathematics (B.S.) and Economics (B.S.) and a minor in Computer Science.

Contact me: nellisa (at) umich (dot) edu

Office: East Hall 4848