Algorithmic Collusion in Electronic Markets: The Impact of Tick Size
66 Pages Posted: 11 May 2022 Last revised: 3 Oct 2022
Date Written: May 10, 2022
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