Diffusion Learning Over Adaptive Competing Networks

In this paper, we study a dynamic game between two networks. The networks compete by optimizing two coupled objective functions. Agents within the same network work toward a common goal and are regarded as cooperative agents; they exchange their strategies via links with other agents. Additionally, in the assumed model, each agent receives information from some adversary agents following a bipartite cross-network topology. The networks employ a diffusion learning strategy that allows them to learn and pursue the equilibrium state adaptively. We show that the networks converge to the Nash equilibrium in the mean-square-error sense under some reasonable assumptions.