A mean-field game of market-making against strategic traders

TL;DR

This paper develops a mean-field game model for market-making where strategic traders influence the market-maker's quoting strategy, incorporating their behaviors and impact on prices through coupled HJB--Fokker--Planck equations.

Contribution

It introduces a novel mean-field game framework for market-making with strategic traders, extending existing models to include trader interactions and price impact.

Findings

Derived optimal controls for market-maker and traders.

Model captures strategic trader behaviors and their influence on prices.

Flexible framework for different trader strategies.

Abstract

We design a market-making model \`a la Avellaneda-Stoikov in which the market-takers act strategically, in the sense that they design their trading strategy based on an exogenous trading signal. The market-maker chooses her quotes based on the average market-takers' behaviour, modelled through a mean-field interaction. We derive, up to the resolution of a coupled HJB--Fokker--Planck system, the optimal controls of the market-maker and the representative market-taker. This approach is flexible enough to incorporate different behaviours for the market-takers and takes into account the impact of their strategies on the price process.