Long-run behavior of games with many players

TL;DR

This paper explores the long-term dynamics of large-player games, examining how increasing players or noise influences equilibrium stability and phase transitions in stochastic systems.

Contribution

It provides a comparative analysis of multi-agent game dynamics and particle systems, highlighting how system size and noise affect stability and phase transitions.

Findings

Increasing players or noise can cause transitions between equilibria.

Stochastic stability of Nash equilibria depends on system parameters.

Examples demonstrate phase transitions in population behavior.

Abstract

We discuss similarities and differencies between systems of many interacting players maximizing their individual payoffs and particles minimizing their interaction energy. We analyze long-run behavior of stochastic dynamics of many interacting agents in spatial and adaptive population games. We review results concerning the effect of the number of players and the noise level on the stochastic stability of Nash equilibria. In particular, we present examples of games in which when the number of players or the noise level increases, a population undergoes a transition between its equilibria.