Abstract
How to predict and control the collective decision-making dynamics in networked populations is of great significance for various applications in engineering, social and natural sciences, and attracts burgeoning interdisciplinary researches across networked systems and control theory. In this paper, we investigate the asynchronous best-response dynamics in networks of anticoordinating agents. To identify the influence of threshold of the anticoordinating model, we consider the homogeneous-threshold networks and explore how the threshold affects the convergence time and network equilibrium. Results on the convergence time show that upper bound of the total number of strategy switches is determined by three factors: the number of network edges, the number of network nodes, and the value of network threshold. Based on the Lyapunov method, asymptotic stability analyses of the network equilibrium are performed. Meanwhile, by introducing relevant payoff incentives (i.e., reward or punishment) during the game playing, the maximal anticoordinating equilibrium with neighboring agents in different strategies will be achieved in finite time to acquire more stable system-wide outcomes.
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