Signal amplification in an agent-based herding model

TL;DR

This paper investigates how external signals, like advertising or public perception, can be amplified through resonance in an agent-based herding model, revealing conditions for optimal response in financial decision-making systems.

Contribution

It extends a stochastic herding model to include external influences and analyzes the resonance phenomena that amplify signals in financial agent interactions.

Findings

Maximum system response occurs at specific noise levels.

Resonance enhances the agents' ability to follow periodic signals.

External signals can significantly influence collective trading behaviors.

Abstract

A growing part of the behavioral finance literature has addressed some of the stylized facts of financial time series as macroscopic patterns emerging from herding interactions among groups of agents with heterogeneous trading strategies and a limited rationality. We extend a stochastic herding formalism introduced for the modeling of decision making among financial agents, in order to take also into account an external influence. In particular, we study the amplification of an external signal imposed upon the agents by a mechanism of resonance. This signal can be interpreted as an advertising or a public perception in favor or against one of the two possible trading behaviors, thus periodically breaking the symmetry of the system and acting as a continuously varying exogenous shock. The conditions for the ensemble of agents to more accurately follow the periodicity of the signal are studied, finding a maximum in the response of the system for a given range of values of both the noise and the frequency of the input signal.