Reinforcement Learning and Nonparametric Detection of Game-Theoretic Equilibrium Play in Social Networks

TL;DR

This paper introduces a reinforcement learning algorithm for social networks to learn equilibrium strategies and a non-parametric test to detect if agents' actions align with game-theoretic equilibrium play, with applications in energy markets and social networks.

Contribution

It proposes a novel diffusion-based reinforcement learning algorithm for social networks and a non-parametric detection method for equilibrium play, integrating economic theory and statistical testing.

Findings

Agents converge to correlated equilibria using the proposed learning algorithm.

The detection test effectively identifies equilibrium behavior in social network data.

Real-world and simulated examples demonstrate the methods' applicability.

Abstract

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.