Iterative Schemes for Markov Perfect Equilibria

TL;DR

This paper develops iterative algorithms to compute Markov perfect equilibria in continuous-time symmetric games, demonstrating convergence and efficiency through theoretical proofs and numerical experiments.

Contribution

It introduces convergence proofs for Picard iteration methods solving the master equation in finite-state Markov games, enabling efficient equilibrium computation.

Findings

Picard iterations converge to the unique solution of the master equation.

Numerical experiments show the algorithms are effective and computationally efficient.

The approach provides a practical method for equilibrium computation in finite-state games.

Abstract

We study Markov perfect equilibria in continuous-time dynamic games with finitely many symmetric players. The corresponding Nash system reduces to the Nash-Lasry-Lions equation for the common value function, also known as the master equation in the mean-field setting. In the finite-state space problems we consider, this equation becomes a nonlinear ordinary differential equation admitting a unique classical solution. Leveraging this uniqueness, we prove the convergence of both Picard and weighted Picard iterations, yielding efficient computational methods. Numerical experiments confirm the effectiveness of algorithms based on this approach.