Strategy Consensus of Evolutionary Games on Networks With Degree-Based Pinning and Incentive Control

This article proposes a novel method to achieve strategy consensus for evolutionary games on networks through degree-based pinning and incentive control. First, for 2-strategy evolutionary games on star networks, the necessary and sufficient condition is proposed to achieve strong strategy consensus only using degree-based pinning control. If this condition is not satisfied, the integration of the incentive control method is explored. This integration yields the minimum value of incentive parameter required to achieve strong strategy consensus. Second, for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$ k $</tex-math></inline-formula>-strategy evolutionary games on star networks, the necessary and sufficient condition only using degree-based pinning control and the minimum value of incentive parameter are proposed to achieve strong strategy consensus. Third, a hierarchical approach for players is employed to extend these results to evolutionary games on general networks. Under the framework of degree-based pinning control, the algorithm for calculating the minimum value of incentive parameter is introduced to make evolutionary games on general networks achieve weak strategy consensus. Finally, two illustrative examples are employed to demonstrate the effectiveness of the obtained results.