Asynchronous best-response dynamics of networked anti-coordination game with payoff incentives

Abstract

How to understand and model the spatial collective decision-making behaviors in the evolutionary game context is an open problem, which attracts burgeoning interdisciplinary studies in the fields of graph theory and evolutionary game theory. This is a newly emerging research topic with wide applications under many real engineering, social and natural nonlinear systems. In this paper, we investigate the asynchronous best-response dynamics of anti-coordinating agents by developing two types of payoff incentive mechanisms, i.e., reward and punishment. We start from characterizing the equilibria of the best-response dynamics based on various types of graph structures. By offering relevant payoff incentives to targeted nodes, we further explore the global outcomes of strategy evolution. Current results suggest that both the reward and punishment can cause the strategy switches of targeted nodes, thus to induce a cascading effect of the evolutionary dynamics in the spatial gaming systems. Given the unlimited and limited budget cases for the payoff incentives, we calculate the optimal solutions for the added incentives, which facilitates the prediction on how the system dynamics be influenced by the proposed incentive mechanisms.