PAC Algorithms for Detecting Nash Equilibrium Play in Social Networks: From Twitter to Energy Markets

The detection of agents whose responses satisfy equilibrium play is useful for predicting the dynamics of information propagation in social networks. Using Afriat's theorem of revealed preferences, we construct a non-parametric detection test to detect if the responses of a group of agents is consistent with play from the Nash equilibrium of a concave potential game. For agents that satisfy the detection test, it is useful to learn the associated concave potential function of the game. In this paper, a non-parametric learning algorithm is provided to estimate the concave potential function of agents with necessary and sufficient conditions on the response class for the algorithm to be a probably approximately correct learning algorithm. In the case of response signals measured in noise, a statistical test to detect agents playing a concave potential game that has a pre-specified Type-I error probability is provided. The detection tests and learning algorithm are applied to real-world data sets from the Twitter social network and the Ontario power grid.