# Optimal make take fees in a multi market maker environment

## TL;DR

This paper models an exchange's optimal contract with multiple market makers using a principal-agent framework, deriving explicit solutions and revealing that more market makers are not always better for liquidity.

## Contribution

It introduces a multi-market maker model with explicit optimal contract and spread policies, highlighting new phenomena like the limited benefit of increasing market makers.

## Key findings

- Explicit optimal contract form derived
- Optimal spread policies for market makers identified
- More market makers are not always optimal for liquidity

## Abstract

Following the recent literature on make take fees policies, we consider an exchange wishing to set a suitable contract with several market makers in order to improve trading quality on its platform. To do so, we use a principal-agent approach, where the agents (the market makers) optimise their quotes in a Nash equilibrium fashion, providing best response to the contract proposed by the principal (the exchange). This contract aims at attracting liquidity on the platform. This is because the wealth of the exchange depends on the arrival of market orders, which is driven by the spread of market makers. We compute the optimal contract in quasi explicit form and also derive the optimal spread policies for the market makers. Several new phenomena appears in this multi market maker setting. In particular we show that it is not necessarily optimal to have a large number of market makers in the presence of a contracting scheme.