A Simple Learning Rule for Resilient Nash Equilibria

We consider scenarios where distributed agents are imperfect and occasionally adopt incorrect actions by mistake. Our goal is to design a distributed learning rule that allows the agents to seek resilient pure-strategy Nash equilibria (PSNEs) that can tolerate deviations potentially by multiple agents. We propose a new learning rule with a tunable parameter for pursuing resilient PSNEs, called Simple Experimentation with Monitoring (SEM). We prove that, when all agents adopt the SEM rule, the only stochastically stable states are PSNEs with a certain tunable level of resilience.