Temporal oscillations and phase transitions in the evolutionary minority game

TL;DR

This paper investigates the dynamic behavior of adaptive agents in the minority game, revealing that their winning probabilities oscillate over time and that these oscillations influence phase transitions between self-segregation and clustering.

Contribution

It demonstrates that the system does not reach a true stationary state but exhibits temporal oscillations in winning probabilities, explaining the phase transition phenomena.

Findings

Winning probabilities show temporal oscillations.

Oscillation characteristics depend on prize-to-fine ratio R.

Oscillations explain the transition from self-segregation to clustering.

Abstract

The study of societies of adaptive agents seeking minority status is an active area of research. Recently, it has been demonstrated that such systems display an intriguing phase-transition: agents tend to {\it self-segregate} or to {\it cluster} according to the value of the prize-to-fine ratio, $R$. We show that such systems do {\it not} establish a true stationary distribution. The winning-probabilities of the agents display temporal oscillations. The amplitude and frequency of the oscillations depend on the value of $R$. The temporal oscillations which characterize the system explain the transition in the global behavior from self-segregation to clustering in the $R<1$ case.