Seminar: Finding an Empirical Equilibrium by Machine Learning in a Pricing Game

Abstract:  We apply machine learning to a classical multi-period pricing game. The game is a duopoly with demand inertia, introduced by Selten in 1965 and studied around 1990 with economic experiments. Its strategies are too complex to represent explicitly. Unlike standard multi-agent reinforcement learning of training agents against each other, our framework is that of a Policy-Space Response Oracle (PSRO) and the "double oracle" method. A few initial strategies that play against each other define a "meta-game". A Nash equilibrium of this meta-game is computed and defines the training environment for a learning agent. Once the agent is sufficiently trained to get a higher payoff than in the current equilibrium, it is added as a new strategy to the meta-game, which expands in this way, and the process repeats. Various learning methods such as SAC (Soft Actor Critic) and PPO (Proximal Policy Optimisation) lead to different limit equilibria in this setup, namely either competitive pricing or cooperative price collusion in the duopoly.

Bio:  Bernhard von Stengel is Professor of Mathematics at the London School of Economics which he joined in 1998, after studies in Germany and the USA. He has been communications officer of the Game Theory Society, and was program chair of the GAMES 2016 congress in Maastricht. He is interested in mathematical questions of game theory. The geometry and computation of Nash equilibria is one of his research specialities.