Two Person Infinite Game of Perfect Information

Given a Game Tree , its Game Space and a set , we define to be the two person infinite game of perfect information.

Interpretation

Player I and Player II play moves alternating (I plays even indices, while II plays odd ones). At each stage, they can only play moves such that the finite sequence of moves played so far is in . After moves, we have a sequence . Then we say that I wins if , while II wins if .