Pricing Personalized Preferences for Privacy Protection in Constant Function Market Makers

TL;DR

This paper introduces a personalized privacy-preserving mechanism for constant function market makers (CFMMs), balancing privacy with arbitrage and truthfulness, and characterizes when such mechanisms are priceable based on noise properties.

Contribution

It proposes a novel noisy CFMM mechanism with personalized privacy fees and characterizes the conditions for priceability and truthfulness based on added noise.

Findings

Priceable mechanisms require zero-mean noise in asset amounts.

Personalized privacy fees are inversely proportional to liquidity.

Adding noise introduces arbitrage opportunities.

Abstract

Constant function market makers (CFMMs) are a popular decentralized exchange mechanism and have recently been the subject of much research, but major CFMMs give traders no privacy. Prior work proposes randomly splitting and shuffling trades to give some privacy to all users [Chitra et al. 2022], or adding noise to the market state after each trade and charging a fixed `privacy fee' to all traders [Frongillo and Waggoner 2018]. In contrast, we propose a noisy CFMM mechanism where users specify personal privacy requirements and pay personalized fees. We show that the noise added for privacy protection creates additional arbitrage opportunities. We call a mechanism priceable if there exists a privacy fee that always matches the additional arbitrage loss in expectation. We show that a mechanism is priceable if and only if the noise added is zero-mean in the asset amount. We also show that priceability and setting the right fee are necessary for a mechanism to be truthful, and that this fee is inversely proportional to the CFMM's liquidity.