Bio-inspired Evolutionary Game Dynamics on Complex Networks under Uncertain Cross-inhibitory Signals

TL;DR

This paper models how populations reach consensus between two options using bio-inspired evolutionary game theory, considering network effects and uncertain signals, with applications in honeybee behavior and opinion dynamics.

Contribution

It introduces a novel evolutionary game model for honeybee-like behavior, analyzes stability and equilibrium, and extends results to complex networks with uncertain parameters.

Findings

Consensus is influenced by network connectivity.

Stable equilibrium exists under certain conditions.

Uncertain cross-inhibitory signals can be managed for stability.

Abstract

Given a large population of players, each player has three possible choices between option 1 or 2 or no option. The two options are equally favorable and the population has to reach consensus on one of the two options quickly and in a distributed way. The more popular an option is, the more likely it is to be chosen by uncommitted players. Uncommitted players can be attracted by those committed to any of the other two options through a cross-inhibitory signal. This model originates in the context of honeybees swarms, and we generalize it to duopolistic competition and opinion dynamics. The contributions of this work include (1) the formulation of an evolutionary game model to explain the behavioral traits of the honeybees, (2) the study of the individuals and collective behavior including equilibrium points and stability, (3) the extension of the results to the case of structured environment via complex network theory, (4) the analysis of the impact of the connectivity on consensus, and (5) the study of absolute stability for the collective system under time-varying and uncertain cross-inhibitory parameter.