Algorithmic Collusion in Electronic Markets: The Impact of Tick Size

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: 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