visualized through the following diagram, in which the moves are made from left to right, with the moves of player I above and the moves of player II below.

The play continues without end, so that a single play of the game determines an infinite sequence of elements of A. The set of all such sequences is denoted A^ω. The players are aware, from the beginning of the game, of a fixed payoff set (a.k.a. winning set) that will determine who wins. The payoff set is a subset of A^?.