Arbitrage on Decentralized Exchanges

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.

Figures (14)

• Figure 1: The quantity $(1-O^{-1/2})^2-\hat{z}$ with respect to the size of the price discrepancy $O$.
• Figure 2: Probability of choosing to revert transactions as a function of inventory risk aversion $\gamma$ in the selectable-revert setting. Parameter values are given in Table \ref{['tab:ParameterValues']}, with $O=1.00074$ in the left panel and $O=1.00213$ in the right panel.
• Figure 3: $\rho^*$ (right axis), $\phi^*$ (left panel, left axis), and $D^{\ell,*}/y$, $\ell\in\{0,\infty\}$ (right panel, right axis) as functions of gas fee $g$ in the selectable-revert setting. Parameter values are given in Table \ref{['tab:ParameterValues']}, with $O=1.00074$ and $\gamma=0.64$.
• Figure 4: Trading probability $\alpha^*$ (top-left), expected relative trading amount $D^*_A/y_A$ (top-right), expected gas fee paid (middle-left), probability $\beta^*$ of choosing to revert transactions in the selectable-revert setting (middle-right), expected profit (bottom-left), and probability of no residual arbitrage (bottom-right) as functions of inventory risk aversion $\gamma$. Parameter values are given in Table \ref{['tab:ParameterValues']}. For each value of $O$, we compute each of the six quantities and then average across the ten values of $O$.
• Figure 5: Histogram of priority fees in arbitrage swaps.

Theorems & Definitions (20)

• Definition 2.1: Symmetric Mixed Nash Equilibrium
• Proposition 3.1
• Proposition 3.2
• Theorem 3.1
• Proposition 3.3
• Theorem 3.2
• Proposition 3.4
• Proposition 3.5
• Lemma A.1
• Lemma A.2