Paper: arXiv 2301.08558

Authors: Théodore Conrad, Arthur Vinciguerra, Guillaume Méroué

Abstract

Constant-product market making functions were first introduced by Hayden Adams in 2017 to create Uniswap, a decentralised exchange on Ethereum. This enables users to exchange assets at any given rate. Some variations such as Balancer and Curve were later introduced. In this paper, we analyse the maths that rule this type of protocol. We show that splitting a trade in multiple smaller trades does not impact the final exchange rate. We also show that the protocol is safer and more profitable when no one recompounds their fees.

Complexity vs Empirical Score

  • Math Complexity: 4.5/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Philosophers — conceptual discussion, limited math and data

Why this score: The paper provides a straightforward mathematical formalization of Uniswap-style constant-product market makers and proves basic deterministic properties like path independence of trade splits. However, it lacks empirical validation, empirical transaction data analysis, and advanced quantitative modeling beyond elementary algebraic identities.

Research Flowchart

  flowchart TD
    A[Research Goal: Analyze Math & Incentives of Constant-Product AMMs] --> B[Input: Uniswap Model & Variants e.g., Balancer, Curve]
    B --> C[Method: Mathematical Proofs & Financial Modeling]
    C --> D[Analyze Trade Splitting Effects]
    C --> E[Analyze Fee Recompounding Strategies]
    D --> F[Outcome 1: Trade Splitting Does Not Alter Final Exchange Rate]
    E --> G[Outcome 2: Protocol is Safer & More Profitable Without Fee Recompounding]