An analysis of Uniswap markets

TL;DR

This paper provides a formal analysis of Uniswap's constant product markets, demonstrating their ability to closely track market prices and exhibit stability under various conditions through simulations.

Contribution

It offers the first formal proof of Uniswap's price tracking properties and validates its stability with large-scale simulations.

Findings

Uniswap closely tracks reference market prices under common conditions.

Uniswap exhibits stability across diverse market scenarios.

The analysis confirms desirable properties of constant product markets.

Abstract

Uniswap -- and other constant product markets -- appear to work well in practice despite their simplicity. In this paper, we give a simple formal analysis of constant product markets and their generalizations, showing that, under some common conditions, these markets must closely track the reference market price. We also show that Uniswap satisfies many other desirable properties and numerically demonstrate, via a large-scale agent-based simulation, that Uniswap is stable under a wide range of market conditions.