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Liquidity Pools as Mean Field Games with Transaction Costs

Agustín Muñoz González

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.

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.
Paper Structure (5 sections, 8 theorems, 56 equations)

This paper contains 5 sections, 8 theorems, 56 equations.

Table of Contents

  1. Introduction
  2. Model Formulation
  3. Does a Mean Field Game Solution Still Exist?
  4. Two Auxiliary Mean Field Games
  5. Back to the Original Problem

Key Result

Corollary 3.1

The following conditions hold:

Theorems & Definitions (20)

  • Remark
  • Remark
  • Corollary 3.1
  • proof
  • Remark 4.1
  • Corollary 4.2
  • proof
  • Corollary 4.3
  • proof
  • Corollary 4.4
  • ...and 10 more