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

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.