Dynamical models for distributed social power perception in Friedkin-Johnsen influence networks

Abstract

Social power quantifies the ability of individuals to influence others and plays a central role in social influence networks. Yet, computing social power typically requires global knowledge and significant computational or storage capability, especially in large-scale networks with stubborn individuals. In this paper, we propose a distributed perception mechanism based on the Friedkin-Johnsen opinion dynamics that enables individuals to estimate their true social power through local interactions. The mechanism starts from independent initial perceptions and relies only on local information: each individual only needs to know its neighbors' stubbornness and the influence weights they accord. We provide rigorous dynamical system analysis that characterizes equilibria, invariant sets, and convergence. Conditions are established for convergence to the true social power in both the static setting with fixed influence weights and the reflected-appraisal setting where influence weights coevolve with perceptions. The proposed mechanism remains reliable under extreme initial perceptions, disconnected influence networks, reflected-appraisal coupling, and variations in timescales. Numerical examples illustrate our results.