Liquidity Pools as Mean Field Games with Transaction Costs

TL;DR

This paper extends a mean field game model of liquidity pools by incorporating transaction costs, analyzing how fees influence trader behavior and market equilibrium in constant product protocols.

Contribution

It introduces a new theoretical framework that includes transaction costs into the mean field game model of liquidity pools, establishing solution existence and trader strategies.

Findings

Existence of mean field game solutions with transaction costs

Characterization of traders' optimal strategies under fee impacts

Foundation for future research on market dynamics with costs

Abstract

This paper extends the theoretical framework introduced in Liquidity Pools as Mean Field Games: A New Framework, where the interactions among traders in a constant product market-making protocol were modeled using mean field games (MFG). In this extension, transaction costs are incorporated into the traders' inventory dynamics, modeling the impact of pool fees on trading decisions. Traders operate at a mid-price adjusted for transaction costs, introducing a new dynamic for the DAI inventory. The existence of MFG solutions for this new trader game is established, taking these additional costs into account. The traders' optimization strategies and the conditions for equilibrium existence are discussed, providing a solid foundation for future research.