  In this work, we study the social learning problem, in which agents of a
networked system collaborate to detect the state of the nature based on their
private signals. A novel distributed graphical evolutionary game theoretic
learning method is proposed. In the proposed game-theoretic method, agents only
need to communicate their binary decisions rather than the real-valued beliefs
with their neighbors, which endows the method with low communication
complexity. Under mean field approximations, we theoretically analyze the
steady state equilibria of the game and show that the evolutionarily stable
states (ESSs) coincide with the decisions of the benchmark centralized
detector. Numerical experiments are implemented to confirm the effectiveness of
the proposed game-theoretic learning method.
