On the Minority Game : Analytical and Numerical Studies

TL;DR

This paper provides analytical and numerical insights into the minority game, exploring phase transitions, learning dynamics, evolutionary processes, and the impact of player size on system performance.

Contribution

It offers an analytical expression for the variance in the minority game and analyzes the effects of evolution and player size on outcomes.

Findings

Identified the origin of the phase transition in the game.

Derived an analytical expression for ^M region.

Discovered power-law distribution of player lifetime.

Abstract

We investigate further several properties of the minority game we have recently introduced. We explain the origin of the phase transition and give an analytical expression of $\sigma^2/N$ in the $N\ll2^M$ region. The ability of the players to learn a given payoff is also analyzed, and we show that the Darwinian evolution process tends to a self-organized state, in particular, the life-time distribution is a power-law with exponent -2. Furthermore, we study the influence of identical players on their gain and on the system's performance. Finally, we show that large brains always take advantage of small brains.