Abstract : We
examine the problem of the existence
of optimal deterministic stationary strategies
two-players antagonistic (zero-sum) perfect information
stochastic games with finitely
many states and actions.
We show that
of such strategies follows from the existence of optimal deterministic stationary
strategies for some derived one-player games.
Thus we reduce
the problem from two-player to one-player games (Markov decision
problems), where usually it is much easier to tackle.
The reduction is very general, it holds not only
for all possible payoff mappings but also
in more a general situations where
players' preferences are not expressed by payoffs.