High Quality Content by WIKIPEDIA articles! A parity game is played on a (countable) colored directed graph, where each node has been colored by a priority - one of (usually) finitely many natural numbers. Two players, 0 and 1, take turns moving a token along the edges of the graph, resulting in a (possibly infinite) path, called the play. The winner of a finite play is the player whose opponent is unable to move. The winner of an infinite play is determined by the priorities appearing in the play. Typically, player 0 wins an infinite play if the smallest priority that occurs infinitely often in the play is even. Player 1 wins otherwise. This explains the word "parity" in the title. Parity games lie in the third level of the borel hierarchy, and are consequently determined.

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