Cooperation and synchronization in evolutionary opinion changing rate games

Abstract

Works based on opinion changing rate (OCR) model focused on synchronization due to interactions among oscillators, but the cost of interactions had not been considered. Inspired by the evolutionary Kuramoto dilemma, we reconsider the OCR model with treating the oscillators’ interaction (or not) as their cooperation (defection) strategies. Cooperators pay the cost of interaction and get higher benefits of the local synchronization, while defectors pay nothing and do nothing to improve their local synchronization benefits. The system reaches the highest synchronization level when the balance between the local synchronization and the cooperation cost is met. Before that, increasing the coupling strength or decreasing the cooperation cost mainly improve the local synchronization rather than the global one with an almost complete cooperation profile. After the balance, both increasing the coupling strength and increasing the cost hinders the formation of cooperators’ clusters and no global synchronization can be reached. More interestingly, it is counter intuitively that a smaller range of natural opinion changing rate just supports a smaller range of the global synchronization. In addition, we show that the results of the model are robust to other topologies of underlying networks.