Learning Parametric Monotone Games

We study the problem of learning from data a parametric Nash equilibrium (NE) problem that is monotone (or strongly monotone) for all parameter values. In the presence of local and shared convex constraints, monotonicity enables efficient computation of generalized Nash equilibria of the learned game. We consider two learning scenarios: (i) direct learning of the NE problem from samples of the agents' costs, and (ii) inverse learning of surrogate agents' costs from samples of their best responses. We propose two methods to solve these tasks. The first is a penalty-based approach that promotes monotonicity of the learned game during training. The second, based on a representation theorem we introduce for a broad class of monotone games, parameterizes the agents' costs so that monotonicity of the NE problem is guaranteed by construction, for all parameter values, regardless of the training data used. We illustrate the applicability of the proposed methods on several numerical examples. A Python library and the examples reported in the paper are available at https://github.com/bemporad/learn_monotone_games.