Stability and Performance Analysis of Diffusion Learning for Two-Network Competing Problems

We address key theoretical questions concerning competing diffusion (CD) algorithms [1], which are designed to solve an important class of network game problems. Specifically, we focus on a competition scenario involving two networks, where each network consists of cooperating agents that are partially connected to the other through a subset of intermediate edges. During each interaction round, the networks simultaneously observe partial information about their opponents and adapt their strategies accordingly. Building on the foundations of the CD algorithm, we present first-, second-, and fourth-order mean stability analyses, as well as a mean-square deviation (MSD) analysis, providing useful performance guarantees for network competition scenarios under some mild assumptions. Computer simulations conducted on quadratic games illustrate our theoretical findings.