CONNECTIONS BETWEEN BOUNDED-VARIATION CONTROL AND DYNKIN GAMES

A general result is obtained for the existence of saddle-point in a stochastic game of timing, by exploiting its connection with a bounded-variation control problem. Weak compactness arguments prove the existence of an optimal process for the control problem. It is shown that this optimal process generates a pair of stopping times that constitute a saddle-point for the game, using the method of comparing costs at nearby points by switching paths at appropriate random times.

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