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This paper studies two-player games in continuous time with imperfect public monitoring, where information may arrive both gradually and continuously, governed by a Brownian motion, and abruptly and discontinuously, according to Poisson processes. For this general class of two-player games, we characterize the equilibrium payoff set via a convergent sequence of differential equations. The resulting differential equation takes a different form depending on whether or not incentives can be provided through abrupt information exclusively. Moreover, in the presence of abrupt information, the boundary of the equilibrium payoff set may not be smooth outside the set of static Nash payoffs. Equilibrium strategies that attain extremal payoff pairs as well as their intertemporal incentives are elicitable from the limiting solution.
Keywords: Repeated games, continuous time, information arrival, imperfect observability, equilibrium characterization.