Alvaro Cartea

Title: Algorithmic Collusion in Electronic Markets: The Impact of Tick Size

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 obstructs competition, while a smaller tick lowers trading costs for liquidity takers, but slows the speed of convergence to an equilibrium.