On the role of stubbornness in Nash equilibrium problems

We consider Nash equilibrium (NE) seeking in partial-decision information regimes where the data circulating across the agents’ communication network are affected by the agents’ stubborn behavior. Unlike traditional linear averaging approaches, the communication protocol is here based on a nonlinear, state-dependent dynamics that captures the agents’ biases, which hinders the direct application of standard techniques. Building on the explicit characterization of the convergence rate of the opinion dynamics resulting from the proposed scheme, and leveraging operator theory, we embed the communication pattern into two novel NE seeking algorithms for which we derive rigorous convergence guarantees.