G3Ms:Generalized Mean Market Makers

TL;DR

This paper introduces a new family of Constant Function Market Makers called G3Ms, based on generalized means, which interpolate between existing models and offer improved properties for decentralized finance trading.

Contribution

The paper proposes G3Ms, a parametrized family of CFMMs based on generalized means, extending existing models and demonstrating their advantageous properties in DeFi markets.

Findings

G3Ms interpolate between Arithmetic and Geometric Mean CFMMs.

G3Ms include Gf3Ms based on generalized f-means.

G3Ms exhibit properties superior to traditional CFMMs.

Abstract

In the Decentralized Finance (DeFi) setting, we present a new parametrized family of Constant Function Market Makers (CFMMs) which we call the Generalized Mean Market Makers (G3Ms), based on the generalized means. The G3Ms are intermediate between the Arithmetic Mean and Geometric Mean CFMM models, which G3Ms incorporate as special cases. We also present an extension of the G3Ms, based on the so-called Generalized f-Means, called Generalized f-Mean Market Makers (Gf3Ms). We show in addition that the G3Ms possess certain properties preferable to those exhibited by either the Arithmetic Mean CFMM or the Geometric Mean CFMM alone.