A limit theorem for Markov decision processes
Mathias Staudigl
Journal of Dynamics & Games 2014, 1(4): 639-659 doi: 10.3934/jdg.2014.1.639
In this paper I prove a deterministic approximation theorem for a sequence of Markov decision processes with finitely many actions and general state spaces as they appear frequently in economics, game theory and operations research. Using viscosity solution methods no a-priori differentiabililty assumptions are imposed on the value function.
keywords: Markov decision processes optimal control viscosity solutions weak convergence methods.
On repeated games with imperfect public monitoring: From discrete to continuous time
Mathias Staudigl Jan-Henrik Steg
Journal of Dynamics & Games 2017, 4(1): 1-23 doi: 10.3934/jdg.2017001

Motivated by recent path-breaking contributions in the theory of repeated games in continuous time, this paper presents a family of discrete-time games which provides a consistent discrete-time approximation of the continuous-time limit game. Using probabilistic arguments, we prove that continuous-time games can be defined as the limit of a sequence of discrete-time games. Our convergence analysis reveals various intricacies of continuous-time games. First, we demonstrate the importance of correlated strategies in continuous-time. Second, we attach a precise meaning to the statement that a sequence of discrete-time games can be used to approximate a continuous-time game.

keywords: Continuous-time game theory perfect-public equilibrium weak convergence

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