Pigouvian algorithmic platform design

There are rising concerns that reinforcement algorithms might learn tacit collusion in oligopolistic pricing, and moreover that the resulting ‘black box’ strategies would be difficult to regulate. Here, I exploit a strong connection between evolutionary game theory and reinforcement learning to show when the latter’s rest points are Bayes–Nash equilibria, but also to derive a system of Pigouvian taxes guaranteed to implement an (unknown) socially optimal outcome of an oligopoly pricing game. Finally, I illustrate reinforcement learning of equilibrium play via simulation, which provides evidence of the capacity of reinforcement algorithms to collude in a very simple setting, but the introduction of the optimal tax scheme induces a competitive outcome.