  To identify a stationary action profile for a population of competitive
agents, each executing private strategies, we introduce a novel active-learning
scheme where a centralized external observer (or entity) can probe the agents'
reactions and recursively update simple local parametric estimates of the
action-reaction mappings. Under very general working assumptions (not even
assuming that a stationary profile exists), sufficient conditions are
established to assess the asymptotic properties of the proposed active learning
methodology so that, if the parameters characterizing the action-reaction
mappings converge, a stationary action profile is achieved. Such conditions
hence act also as certificates for the existence of such a profile. Extensive
numerical simulations involving typical competitive multi-agent control and
decision-making problems illustrate the practical effectiveness of the proposed
learning-based approach.
