Large-scale games in large-scale systems

TL;DR

This paper reviews recent advances in analyzing large-scale stochastic games by leveraging mean field theory and dynamical systems, simplifying complexity in systems with vast state and action spaces.

Contribution

It provides an overview of recent developments in large-scale games, focusing on population, stochastic population, and mean field stochastic games, with a focus on long-term payoff analysis.

Findings

Mean field limits can be described by deterministic or stochastic equations.

Long-term payoffs are characterized using Bellman and Kolmogorov equations.

The approach reduces complexity in large-scale systems analysis.

Abstract

Many real-world problems modeled by stochastic games have huge state and/or action spaces, leading to the well-known curse of dimensionality. The complexity of the analysis of large-scale systems is dramatically reduced by exploiting mean field limit and dynamical system viewpoints. Under regularity assumptions and specific time-scaling techniques, the evolution of the mean field limit can be expressed in terms of deterministic or stochastic equation or inclusion (difference or differential). In this paper, we overview recent advances of large-scale games in large-scale systems. We focus in particular on population games, stochastic population games and mean field stochastic games. Considering long-term payoffs, we characterize the mean field systems using Bellman and Kolmogorov forward equations.