  This paper studies two important signal processing aspects of equilibrium
behavior in non-cooperative games arising in social networks, namely,
reinforcement learning and detection of equilibrium play. The first part of the
paper presents a reinforcement learning (adaptive filtering) algorithm that
facilitates learning an equilibrium by resorting to diffusion cooperation
strategies in a social network. Agents form homophilic social groups, within
which they exchange past experiences over an undirected graph. It is shown
that, if all agents follow the proposed algorithm, their global behavior is
attracted to the correlated equilibria set of the game. The second part of the
paper provides a test to detect if the actions of agents are consistent with
play from the equilibrium of a concave potential game. The theory of revealed
preference from microeconomics is used to construct a non-parametric decision
test and statistical test which only require the probe and associated actions
of agents. A stochastic gradient algorithm is given to optimize the probe in
real time to minimize the Type-II error probabilities of the detection test
subject to specified Type-I error probability. We provide a real-world example
using the energy market, and a numerical example to detect malicious agents in
an online social network.
