Defensive Rebalancing for Automated Market Makers

2026-01-26

AI Summary

This work addresses the issue of value leakage in constant-function automated market makers (CFMMs) caused by arbitrage opportunities. The authors propose a defensive rebalancing mechanism that directly transfers assets across liquidity pools to transform arbitrage-prone states into no-arbitrage configurations. The key innovation lies in establishing, for the first time, an equivalence between rebalancing and Pareto efficiency, and formulating the optimal no-arbitrage rebalancing problem as a convex optimization task. Furthermore, they design a hybrid rebalancing strategy capable of capturing arbitrage profits from non-participating entities and centralized exchanges. Theoretically, the authors prove that any arbitrage-prone pool configuration can be strictly improved—enhancing liquidity for some CFMMs without harming others—and that for common CFMMs, such as the constant-product model, a unique and efficiently computable optimal solution exists.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Search and Optimization: Learning to Search

Application Category

• Economics, Online Markets and Human Computation: Architectures and workflows that use LLMs for crowd work
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Cryptocurrency and smart contracts

Abstract

This paper introduces and analyzes \emph{defensive rebalancing}, a novel mechanism for protecting constant-function market makers (CFMMs) from value leakage due to arbitrage. A \emph{rebalancing} transfers assets directly from one CFMM's pool to another's, bypassing the CFMMs'standard trading protocols. In any \emph{arbitrage-prone} configuration, we prove there exists a rebalancing to an \textit{arbitrage-free} configuration that strictly increases some CFMMs'liquidities without reducing the liquidities of the others. Moreover, we prove that a configuration is arbitrage-free if and only if it is \emph{Pareto efficient} under rebalancing, meaning that any further direct asset transfers must decrease some CFMM's liquidity. We prove that for any log-concave trading function, including the ubiquitous constant product market maker, the search for an optimal, arbitrage-free rebalancing that maximizes global liquidity while ensuring no participant is worse off can be cast as a convex optimization problem with a unique, computationally tractable solution. We extend this framework to \emph{mixed rebalancing}, where a subset of participating CFMMs use a combination of direct transfers and standard trades to transition to an arbitrage-free configuration while harvesting arbitrage profits from non-participating CFMMs, and from price oracle market makers such as centralized exchanges. Our results provide a rigorous foundation for future AMM protocols that proactively defend liquidity providers against arbitrage.

Problem

• automated market makers
• arbitrage
• liquidity protection
• constant-function market makers
• value leakage

Innovation

• defensive rebalancing
• constant-function market makers
• arbitrage-free
• convex optimization
• Pareto efficiency