Paper: arXiv 2406.00113

Abstract

Milionis et al.(2023) studied the rate at which automated market makers leak value to arbitrageurs when block times are discrete and follow a Poisson process, and where the risky asset price follows a geometric Brownian motion. We extend their model to analyze another popular mechanism in decentralized finance for onchain trading: Dutch auctions. We compute the expected losses that a seller incurs to arbitrageurs and expected time-to-fill for Dutch auctions as a function of starting price, volatility, decay rate, and average interblock time. We also extend the analysis to gradual Dutch auctions, a variation on Dutch auctions for selling tokens over time at a continuous rate. We use these models to explore the tradeoff between speed of execution and quality of execution, which could help inform practitioners in setting parameters for starting price and decay rate on Dutch auctions, or help platform designers determine performance parameters like block times.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a theoretical model for Dutch auctions on blockchains using geometric Brownian motion and Poisson-distributed block times, deriving closed-form analytical expressions for expected losses and time-to-fill, which indicates high mathematical density. However, the analysis is purely theoretical and simulation-based with no real-world backtesting, empirical data analysis, or implementation details for trading, placing it low on empirical rigor.

Research Flowchart

  flowchart TD
  A["Research Goal"] -->|Analyze| B["Model Extension"]
  B -->|Incorporate| C["Key Parameters"]
  C -->|Apply to| D["Computational Analysis"]
  
  subgraph A ["Research Goal"]
      A1["Trade-off: Speed vs Quality<br>in Dutch Auctions"]
  end
  
  subgraph B ["Methodology"]
      B1["Extend Milionis et al.<br>Discrete-time AMM Model"]
      B2["Analyze Standard<br>Dutch Auctions"]
      B3["Analyze Gradual<br>Dutch Auctions"]
  end
  
  subgraph C ["Key Parameters"]
      C1["Starting Price"]
      C2["Volatility<br>(GBM)"]
      C3["Decay Rate"]
      C4["Poisson Block Time<br>Δt"]
  end
  
  subgraph D ["Computational Processes"]
      D1["Expected Loss to<br>Arbitrageurs"]
      D2["Expected<br>Time-to-Fill"]
  end
  
  subgraph E ["Findings"]
      E1["Parameter Trade-offs:<br>Speed vs Execution Quality"]
      E2["Practical Guidelines for<br>Platform Designers & Users"]
  end

  B --> C
  C --> D
  D --> E