Finite Strategy Switches of Coordinating and Anti-Coordinating Games on Weighted Networks

Complex strategic interactions of rational agents are ubiquitous in decision-making groups which greatly influence the evolutionary dynamics of many real-life networked systems. Here, we study how individual decision-making behaviors evolve when the topology of network interactions is weighted, and how the network of mixed coordinating and anti-coordinating games is driven to an equilibrium. We prove that the weighted pure coordinating or anti-coordinating decision-making dynamics, under both asynchronous and partially synchronous updates, will converge to the Nash equilibrium after finite strategy switches. Moreover, it follows that the upper bound on the number of switches for the convergence depends on the number of agents and the weights' distribution under asynchronous update. For mixed coordinating and anti-coordinating games, we find that network game dynamics can be decoupled into convergence and nonconvergence regions under certain conditions, in which the global convergence can be established by adding leaf vertices. For more general cases, we devise the incentive mechanisms for agents to achieve the convergence. We also extend the incentive performance of fully asynchronous updating to the partially synchronous updating. Our results provide hints on the typology and incentive mechanisms to induce the convergence of mixed gaming networks.