Algorithmic Collusion in Electronic Markets: The Impact of Tick Size

66 Pages Posted: 11 May 2022 Last revised: 3 Oct 2022

See all articles by Álvaro Cartea

Álvaro Cartea

University of Oxford; University of Oxford - Oxford-Man Institute of Quantitative Finance

Patrick Chang

University of Oxford - Oxford-Man Institute of Quantitative Finance

José Penalva

Universidad Carlos III, Madrid - Department of Business Administration

Date Written: May 10, 2022

Abstract

We characterise the stochastic interaction of learning algorithms as a deterministic system of differential equations to understand their long-term behaviour in a repeated game. In a symmetric bimatrix repeated game, we prove that the dynamics of many learning algorithms converge to the outcomes of pure strategy Nash equilibria of the stage game. In market making, we show that the algorithms tacitly collude to extract rents and tick size (coarseness of price grid) matters: a large tick size obstructs competition, while a smaller tick size lowers trading costs for liquidity takers, but slows the speed of convergence to an equilibrium.

Keywords: Artificial Intelligence, Tacit Collusion, Evolutionary Game Theory, Market Making, Limit Order Books, Tick Size

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

Suggested Citation

Cartea, Álvaro and Chang, Patrick and Penalva, José, Algorithmic Collusion in Electronic Markets: The Impact of Tick Size (May 10, 2022). Available at SSRN: https://ssrn.com/abstract=4105954 or http://dx.doi.org/10.2139/ssrn.4105954

Álvaro Cartea

University of Oxford ( email )

Mansfield Road
Oxford, Oxfordshire OX1 4AU
United Kingdom

University of Oxford - Oxford-Man Institute of Quantitative Finance ( email )

Eagle House
Walton Well Road
Oxford, Oxfordshire OX2 6ED
United Kingdom

Patrick Chang

University of Oxford - Oxford-Man Institute of Quantitative Finance ( email )

Eagle House
Walton Well Road
Oxford, Oxfordshire OX2 6ED
United Kingdom

José Penalva (Contact Author)

Universidad Carlos III, Madrid - Department of Business Administration ( email )

Calle Madrid 126
Getafe, 28903
Spain

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