We study two-player games of infinite duration that are played on finite or infinite game graphs. Such a game is*determined*if, from each position, one of the two players has a winning strategy. On the basis of the axiom of choice it is not difficult to prove that there exist nondetermined games. The classical theory of infinite games in descriptive set theory links determinacy of games with topological properties of the winning conditions. Usually the format of Gale-Stewart games is used where the two players strictly alternate, and in each move a player selects an element of {0, 1};