Title: "An axiom of weak determinacy"

We consider a generalization of the concept of an infinte two person game.
The generalization is as follows, instead of playing omega long runs of
natural numbers, the players play \kappa long runs of smaller than \kappa
ordinals, where \kappa is some regular cardinal, so that the resulting
sequence is a member of the set \kappa to the power of \kappa.
As the full axiom of determinacy AD is inconsistent in this case, we
consider a weaker version (AWD) and try to generalize consequences of the
ordinary AD and AD_R to this new context.
The talk will include a characterization of the property "Player X wins"
for some variants of the game, some simple consequences of AWD as well as
some open questions.