Arbitrage on Decentralized Exchanges

ArXiv ID: 2507.08302 “View on arXiv”

Authors: Xue Dong He, Chen Yang, Yutian Zhou

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.

Keywords: Decentralized Exchange, Arbitrage, Gas Fee Competition, Nash Equilibrium, Game Theory, Cryptocurrency

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail
• Why: The paper develops a rigorous game-theoretic model with symmetric mixed Nash equilibrium, involving strategic gas fee competition, which requires advanced mathematical derivation. It complements this with extensive empirical validation using real blockchain data (Binance and Uniswap), backtesting implications like trade frequency, gas fee selection, and profit analysis, making it highly data- and implementation-heavy.

  flowchart TD
    A["Research Goal"] --> B["Game Theoretic Model"]
    B --> C["Data & Assumptions"]
    C --> D["Solve Mixed Nash Equilibrium"]
    D --> E["Computational Analysis"]
    E --> F["Key Findings & Outcomes"]
    
    subgraph C ["Data & Inputs"]
        C1["Liquidity"]
        C2["Gas Fee Costs"]
        C3["Arbitrage Opportunity"]
    end
    
    subgraph E ["Computational Processes"]
        E1["Simulate Trading Decisions"]
        E2["Calculate Expected Profits"]
    end
    
    subgraph F ["Outcomes"]
        F1["No trade for small opportunities"]
        F2["Lower prob for higher gas fees"]
        F3["Higher fees & trade for large opportunities"]
        F4["Profit increases with opp & liquidity"]
    end