A Myopic Adjustment Process for Mean Field Games with Finite State and Action Space

TL;DR

This paper introduces a myopic adjustment process for finite state and action mean field games, demonstrating local convergence to equilibria and global convergence in two-strategy cases, simplifying equilibrium computation.

Contribution

It proposes a natural learning rule for mean field games that converges under broad conditions, addressing computational complexity issues.

Findings

Convergence of the process to stationary equilibria.

Global convergence in two-strategy scenarios.

Broad conditions for local convergence.

Abstract

In this paper, we introduce a natural learning rule for mean field games with finite state and action space, the so-called myopic adjustment process. The main motivation for these considerations are the complex computations necessary to determine dynamic mean-field equilibria, which make it seem questionable whether agents are indeed able to play these equilibria. We prove that the myopic adjustment process converges locally towards stationary equilibria with deterministic equilibrium strategies under rather broad conditions. Moreover, for a two-strategy setting, we also obtain a global convergence result under stronger, yet intuitive conditions.