Dynamics of Market Making Algorithms in Dealer Markets: Learning and Tacit Collusion

Mathematical Finance

43 Pages Posted: 8 Jun 2022 Last revised: 2 Jun 2023

See all articles by Rama Cont

Rama Cont

University of Oxford

Wei Xiong

University of Oxford

Date Written: May 25, 2022

Abstract

The widespread use of market-making algorithms in electronic over-the-counter markets may give rise to unexpected effects resulting from the autonomous learning dynamics of these algorithms. In particular the possibility of `tacit collusion' among market makers has increasingly received regulatory scrutiny.

We model the interaction of market makers in a dealer market as a stochastic differential game of intensity control with partial information and study the resulting dynamics of bid-ask spreads. Competition among dealers is modeled as a Nash equilibrium, while collusion is described in terms of Pareto optima. Using a decentralized multi-agent deep reinforcement learning algorithm to model how competing market makers learn to adjust their quotes, we show that the interaction of market making algorithms via market prices, without any sharing of information, may give rise to tacit collusion, with spread levels strictly above the competitive equilibrium level.

Keywords: Market microstructure, intensity control, differential games, reinforcement learning, market making, tacit collusion, Nash equilibrium, multi-agent actor-critic algorithm, decentralized learning

JEL Classification: D21, D43, D83, L12, L13

Suggested Citation

Cont, Rama and XIONG, Wei, Dynamics of Market Making Algorithms in Dealer Markets: Learning and Tacit Collusion (May 25, 2022). Mathematical Finance, Available at SSRN: https://ssrn.com/abstract=4119858 or http://dx.doi.org/10.2139/ssrn.4119858

Rama Cont (Contact Author)

University of Oxford ( email )

Mathematical Institute
Oxford, OX2 6GG
United Kingdom

HOME PAGE: http://www.maths.ox.ac.uk/people/rama.cont

Wei XIONG

University of Oxford ( email )

Radcliffe Observatory, Andrew Wiles Building
Woodstock Rd
Oxford, Oxfordshire OX2 6GG
United Kingdom

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