Numerical Simulations of Continuous-Time Flows for Monotone Games

Abstract

In this paper, we formulate three numerical algorithms for approximating Nash equilibria in monotone finite and mean-field games based on theoretical results that demonstrate convergence of ODE, Cesaro mean and gradient descent methods. Using a few example games, we compare convergence based on different game properties like strong monotonicity and symmetry; since our algorithms are based on Euler’s method, a linearization based on the Jacobian allows us to analyze the underlying structure of each game and how the error converges. In algorithms involving noise, we are also able to determine a more accurate noise floor based on this analysis.