Convergence Rates and Collusive Outcomes of Pricing Algorithms

Artificial intelligence algorithms are increasingly used by firms to set prices. Previous research on pricing algorithms shows that they can exhibit collusive behavior, but it has so far remained an open question whether they can do so in a reasonably short time. I develop a deep reinforcement learning model able to price goods in a repeated oligopolistic competition game with continuous prices that, under reasonable assumptions on the length of a time step, converges to a collusive outcome in an amount of time that matches empirical observations. The model I propose reliably shows cooperative behavior supported by reward-punishment schemes that discourage deviations from the point of convergence