Fluctuations around Nash Equilibria in Game Theory

TL;DR

This paper studies how small irrational behaviors can cause large fluctuations around Nash equilibria in large games, revealing stability properties and the influence of multiple equilibria.

Contribution

It introduces a statistical approach to analyze fluctuations and stability of Nash equilibria under irrationality in large games.

Findings

Nash equilibria are weakly stable and susceptible to amplification of irrationality.

Multiple equilibria exist, with some being globally stable.

Characteristic times to reach stable states can be very long.

Abstract

We investigate the fluctuations induced by irrationality in simple games with a large number of competing players. We show that Nash equilibria in such games are ``weakly'' stable: irrationality propagates and amplifies through players' interactions so that huge fluctuations can results from a small amount of irrationality. In the presence of multiple Nash equilibria, our statistical approach allows to establish which is the globally stable equilibrium. However characteristic times to reach this state can be very large.