Arbitrage on Decentralized Exchanges

2025-07-11

AI Summary

This paper investigates on-chain arbitrage driven by exchange rate discrepancies between decentralized exchanges (DEXs) and centralized exchanges (CEXs), focusing on strategic interactions among arbitrageurs under gas fee competition. Method: We formulate a two-player gas fee bidding game and rigorously establish the existence and uniqueness of a symmetric mixed-strategy Nash equilibrium. Contribution/Results: Our theoretical analysis yields several counterintuitive insights—e.g., arbitrageurs may voluntarily forgo small arbitrage opportunities, and higher gas bids occur with lower probability under larger opportunities. We show that both arbitrage opportunity size and liquidity depth increase bid frequency and magnitude, thereby raising expected profits. Empirical validation using on-chain transaction data confirms the robustness of our model’s predictions. To our knowledge, this is the first work to formalize gas fee competition as an incomplete-information bidding game, offering a novel paradigm for analyzing DeFi arbitrage dynamics and market efficiency.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Search and Optimization: Learning to Search

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Security and Privacy: Cryptocurrency and smart contracts
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Decentralized exchanges (DEXs) are alternative venues to centralized exchanges (CEXs) for trading cryptocurrencies and have become increasingly popular. An arbitrage opportunity arises when the exchange rate of two cryptocurrencies in a DEX differs from that in a CEX. Arbitrageurs can then trade on the DEX and CEX to make a profit. Trading on the DEX incurs a gas fee, which determines the priority of the trade being executed. We study a gas-fee competition game between two arbitrageurs who maximize their expected profit from trading. We derive the unique symmetric mixed Nash equilibrium and find that (i) the arbitrageurs may choose not to trade when the arbitrage opportunity and liquidity is small; (ii) the probability of the arbitrageurs choosing a higher gas fee is lower; (iii) the arbitrageurs pay a higher gas fee and trade more when the arbitrage opportunity becomes larger and when liquidity becomes higher; (iv) the arbitrageurs' expected profit could increase with arbitrage opportunity and liquidity. The above findings are consistent with our empirical study.

Problem

• Analyzes gas-fee competition between arbitrageurs on DEXs vs CEXs
• Examines how arbitrageurs maximize profits under varying market conditions
• Studies impact of liquidity and arbitrage size on trading behavior

Innovation

• Analyzes gas-fee competition game between arbitrageurs
• Derives unique symmetric mixed Nash equilibrium
• Empirically validates findings on arbitrage behavior