On Arbitrage in Single- and Multi-token Uniswap Markets

Abstract

Uniswap and other constant product market makers have proven to be popular decentralized cryptocurrency exchanges, despite their simplicity. However, the exchange rate between pairs of currencies need not be consistent across the entire Uniswap market, and such price discrepancies open up the possibility of arbitrage. In this paper, we propose a theoretical examination into the possibility of efficient arbitrage in single- and multi-token Uniswap markets. We construct a polynomial-time cyclic arbitrage algorithm for single-token Uniswap markets and give insights into the state of the market after arbitrage. We then generalize to multi-token Uniswap markets by constructing a linear program that allows the arbitrage of asset bundles. After arbitraging the market, we then extend results by Goyal et al. (2023) to provide an optimal liquidity provision strategy for a Uniswap market. This provides a pipeline for an arbitrageur: they first extract profit from the market via arbitrage, and then they may reinvest their profits back into the market in the form of liquidity provision. Finally, we conclude with an empirical study into the profitability of arbitrage in historical Uniswap markets.