Dynamical instabilities in a simple minority game with discounting

TL;DR

This paper investigates how discounting and experimentation influence the dynamics of a simple minority game, revealing that certain parameter changes can cause large fluctuations due to dynamical instabilities.

Contribution

It introduces a minimal model of adaptive agents with discounting and experimentation, analyzing how these factors induce phase transitions and instabilities in the system.

Findings

Large fluctuations emerge at dynamical bifurcations.

Instabilities can be discontinuous or continuous depending on parameters.

Noise amplification near bifurcations drives the instability.

Abstract

We explore the effect of discounting and experimentation in a simple model of interacting adaptive agents. Agents belong to either of two types and each has to decide whether to participate a game or not, the game being profitable when there is an excess of players of the other type. We find the emergence of large fluctuations as a result of the onset of a dynamical instability which may arise discontinuously (increasing the discount factor) or continuously (decreasing the experimentation rate). The phase diagram is characterized in detail and noise amplification close to a bifurcation point is identified as the physical mechanism behind the instability.