Abstract
We study the sufficient conditions for the existence of a saddle point of a time-dependent discrete Markov zero-sum game up to a given stopping time. The stopping time is allowed to take either a finite or an infinite non-negative random variable with its associated objective function being well-defined. The result enables us to show the existence of the saddle points of discrete games constructed by Markov chain approximation of a class of stochastic differential games.
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