Speed of Intervention in Algorithmic Markets: Controlling Collusion and Stability

Algorithmic pricing is prevalent in online marketplaces, raising concerns that learning algorithms may sustain supra-competitive outcomes, a phenomenon often referred to as algorithmic collusion. We study two sellers in a repeated Prisoner’s Dilemma who delegate decisions to memoryless value-based learning algorithms. A platform steers demand toward sellers choosing the more competitive action. Using a continuous-time fluid approximation of the learning dynamics, we characterize how intervention intensity, learning architecture, and implementation speed determine market dynamics. Stronger intervention lowers cooperation levels at the fixed point. Algorithmic responsiveness determines the location of stationary outcomes, while action-dependent learning rates determine their local stability. As intervention intensifies, the fixed point can lose stability through a Hopf bifurcation and its local basin of attraction shrinks as the stability threshold is approached. Consequently, an abrupt intervention may leave inherited Q-values outside the target’s local basin of attraction and lead to persistent oscillations, whereas gradual intervention leads to a stable market outcome. We also derive a local bound on implementation speed. Our results show that platform regulation of algorithmic collusion may require choosing not only how much to intervene, but also how quickly to implement the intervention relative to the algorithms’ learning dynamics.