Detection of Homophilic Communities and Coordination of Interacting Meta-Agents: A Game-Theoretic Viewpoint - Gharehshiran, Omid Namvar; Hoiles, William; Krishnamurthy, Vikram (IEEE transactions on signal and information processing over networks, 2016)
This paper studies two important signal processing aspects of homophilic behavior namely, detection of homophilic communities and the distributed coordination of meta-agents, which interact with the detected homophilic communities. First, the theory of revealed preferences from microeconomics is used to construct a nonparametric decision test for homophilic behavior using only the time series of external influences and associated agents' responses. These tests rely on rationalizing the dataset of agents' actions as the play from the Nash equilibrium of a concave potential game. A stochastic gradient algorithm is given to optimize the external influence signal in real time to minimize the Type-II error probabilities of the detection test subject to specified Type-I error probability. Using the decision test, methods are provided to detect for homophilic communities. Subsequently, a nonparametric algorithm is presented that uses the constructed potential function for the potential game to predict the preferences of the detected homophilic communities. Second, we present a non-cooperative game model for interaction of meta-agents that interact with the communities and propose an algorithm that prescribes meta-agents how to take actions based on the preference of the communities and past interaction information with other meta-agents. The proposed algorithm has two timescales: the slow timescale is the nonparametric preference learning presented in the first part, and the fast timescale is a regret-matching stochastic approximation algorithm. It is shown that, if all meta-agents follow the proposed algorithm, their collective behavior is attracted to the correlated equilibria set of the game. This means that meta-agents can co-ordinate their strategies in a distributed fashion as if there exists a centralized coordinating device that they all trust to follow. We provide a real-world example using the energy market, and a numerical example to detect malicious agents in an online social network.