  Non-cooperative games serve as a powerful framework for capturing the
interactions among self-interested players and have broad applicability in
modeling a wide range of practical scenarios, ranging from power management to
drug delivery. Although most existing solution algorithms assume the
availability of first-order information or full knowledge of the objectives and
others' action profiles, there are situations where the only accessible
information at players' disposal is the realized objective function values. In
this paper, we devise a bandit online learning algorithm for merely coherent
games that integrates the optimistic mirror descent scheme and multi-point
pseudo-gradient estimates. We further demonstrate that the generated actual
sequence of play can converge a.s. to a critical point if the sequences of
query radius and sample size are chosen properly, without resorting to extra
Tikhonov regularization terms or additional norm conditions. Finally, we
illustrate the validity of the proposed algorithm via a Rock-Paper-Scissors
game and a least square estimation game.
