Liquidity Pools as Mean Field Games with Transaction 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.