The role of frustration in collective decision-making dynamical processes on multiagent signed networks

TL;DR

This paper investigates how frustration in signed networks influences collective decision-making dynamics, revealing bifurcation behavior where increased social effort leads to community decisions, especially as frustration varies.

Contribution

It introduces a nonlinear dynamical model for multiagent decision-making on signed networks and analyzes how frustration affects bifurcation and decision states.

Findings

Increased social effort induces a pitchfork bifurcation from indecision to decision states.

Higher frustration delays the bifurcation point, requiring more effort for decision-making.

The model captures the impact of network imbalance on collective choices.

Abstract

In this work we consider a collective decision-making process in a network of agents described by a nonlinear interconnected dynamical model with sigmoidal nonlinearities and signed interaction graph. The decisions are encoded in the equilibria of the system. The aim is to investigate this multiagent system when the signed graph representing the community is not structurally balanced and in particular as we vary its frustration, i.e., its distance to structural balance. The model exhibits bifurcations, and a ``social effort'' parameter, added to the model to represent the strength of the interactions between the agents, plays the role of bifurcation parameter in our analysis. We show that, as the social effort increases, the decision-making dynamics exhibits a pitchfork bifurcation behavior where, from a deadlock situation of ``no decision'' (i.e., the origin is the only globally stable equilibrium point), two possible (alternative) decision states for the community are achieved (corresponding to two nonzero locally stable equilibria). The value of social effort for which the bifurcation is crossed (and a decision is reached) increases with the frustration of the signed network.