Some Axioms of Weak Determinacy

We consider two-player games of perfect information of length some
cardinal $\kappa$. It is well-known that for $\kappa \geq \omega_1$
the full axiom of determinacy for these games fails, thus we
investigate three weaker forms of it. We obtain the measurability
of $\kappa^{+}$ under $DC_{\kappa}$-the axiom of dependent choices
generalized to $\kappa$. We generalize the notions of perfect and
meager sets and provide characterizations with some special kinds
of games. We show that under an additional assumption one of our
three axioms follows from the other two.