Arbitrage on Decentralized Exchanges

TL;DR

This paper develops an equilibrium model of arbitrage on decentralized exchanges considering competition among arbitrageurs and transaction reversion settings, revealing impacts on profitability and market efficiency, supported by empirical data.

Contribution

It introduces the first equilibrium model of gas fee competition among arbitrageurs under various transaction reversion scenarios, incorporating competition effects.

Findings

Pure symmetric equilibria do not exist; mixed equilibria are unique.

Low inventory risk favors no-revert setting for arbitrage profits.

High inventory risk favors no-revert and selectable-revert settings for profitability and efficiency.

Abstract

Decentralized exchanges using automated market makers create arbitrage opportunities with centralized exchanges, where gas fees and transaction ordering are critical. Existing models largely overlook competition among arbitrageurs, despite price discrepancies being public information. We develop the first equilibrium model of gas fee competition between two arbitrageurs under three transaction reversion settings: no-revert, auto-revert, and selectable-revert. We show that pure symmetric equilibria do not exist, but unique mixed equilibria can be characterized. Comparative analysis reveals that under low inventory risk, the no-revert setting favors arbitrageurs in terms of profit, while auto-revert and selectable-revert settings enhance market efficiency. Under high inventory risk, the no-revert and selectable-revert settings dominate the auto-revert setting in both profitability and efficiency. Using data from Binance and Uniswap V2, we empirically confirm that arbitrageurs face positive inventory risk and validate our model's implications: gas fees increase with price discrepancies and liquidity, while trading amounts rise with both price discrepancies and gas fees.