Congestion, equilibrium and learning: The minority game

TL;DR

This paper analyzes the minority game, a congestion game where players aim to choose the less popular option, characterizing Nash equilibria and examining how various learning processes predict different outcomes.

Contribution

It provides a comprehensive characterization of Nash equilibria and compares predictions of different learning processes in the minority game with any odd number of players.

Findings

Different learning processes yield significantly different predictions.

The set of Nash equilibria is explicitly characterized.

Behavioral predictions vary notably across learning models.

Abstract

The minority game is a simple congestion game in which the players' main goal is to choose among two options the one that is adopted by the smallest number of players. We characterize the set of Nash equilibria and the limiting behavior of several well-known learning processes in the minority game with an arbitrary odd number of players. Interestingly, different learning processes provide considerably different predictions.