Composing Networks of Automated Market Makers

TL;DR

This paper introduces a mathematical framework for composing automated market makers (AMMs), enabling complex, multi-asset trading systems while maintaining stability and composability in blockchain environments.

Contribution

It defines formal operators for sequential and parallel composition of AMMs, ensuring closure and stability for higher-dimensional multi-asset AMMs.

Findings

Defined composition operators for AMMs

Ensured closure under composition for complex AMMs

Maintained stability in multi-asset AMM networks

Abstract

Automated market makers (AMMs) are automata that trade electronic assets at rates set by mathematical formulas. AMMs are usually implemented by smart contracts on blockchains. In practice, AMMs are often composed: and outputs from AMMs can be directed into other compatible AMMs. This paper proposes a mathematical model for AMM composition. We define sequential and parallel composition operators for AMMs in a way that ensures that AMMs are closed under composition, in a way that works for "higher-dimensional" AMMs that manage more than two asset classes, and so the composition of AMMs in "stable" states remains stable.