Bio-Inspired Evolutionary Game Dynamics in Symmetric and Asymmetric Models

Abstract

A large population of players has to reach consensus in a distributed way between two options. The two options can be equally favorable or one option can have a higher intrinsic value (asymmetric parameters). In both cases, uncommitted players choose one of the two options depending on the popularity of that option, while committed players can be attracted by those committed to the other option via cross-inhibitory signals. We illustrate the model in different application domains including honeybee swarms, duopolistic competition and opinion dynamics. The main contributions of this letter are as follows: 1) we develop an evolutionary game model to explain the behavioral traits of the honeybees where this model originates; 2) we study individuals’ and collective behavior including conditions for local asymptotic stability of the equilibria; 3) we study thresholds on the cross-inhibitory signal for the symmetric case and for the corresponding model with heterogeneous connectivity in the case of asymmetric structure with asymmetric parameters; and 4) we study conditions for stability and passivity properties for the collective system under time-varying and uncertain cross-inhibitory parameter in the asymmetric structure and parameters.