Artificial Multi-Step Ahead Optimal Strategy for Opinion Dynamics with Delayed Decision Making

Social-psychological has provided clear evidence that opinion dynamics and decision making pro cesses are closely intertwined, yet the social phenomenon of delayed decision making in opinion evolution is ubiquitous. However, how to theoretically analyze the opinion dynamics with delayed decision making remains a challenging problem. In this paper, we propose a rigorous theoretical framework for analyzing such opinion dynamics. For opinion dynamics without delayed decision making, we first propose an artificial one-step ahead optimal strategy. Un like the conventional one-step ahead optimal strategy that leverages original opinion model information, our proposed artificial one-step ahead optimal strategy utilizes the artificial opinion model information, and the resulting criteria involve an opinion adjustment matrix and are thus easy to test. Furthermore, for opinion dynamics with delayed decision making, we propose an artificial multi-step ahead optimal strategy. It is revealed that our proposed strategies are able to make the group's opinions converge to the fixed point and approach the prescribed opinions. Additionally, we simultaneously study both synchronous and nested update processes. Finally, we apply our artificial multi-step ahead optimal strategy to analyze two real-life scenarios using Zachary's Karate Club network. It is shown that the opinions achieve consensus and approach the prescribed opinions of coach-centered group, respectively. Two numerical examples are provided to verify the effectiveness of the theoretical findings, one of which compares our proposed artificial multi-step ahead optimal strategy with the conventional one-step ahead optimal strategy.