Talk:Parity game

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The definition given does not match the notion of a "parity game". To my knowledge, a parity game is a two-player board game where board positions are assigned natural numbers, so called priorities. The winner of a finite play in a parity game is the player whose opponent gets stuck. The winner of an infinite play is determined by the priorities of infinitely often occuring board positions. Typically, player 0 wins an infinite play if the highest priority of an infinitely often occuring positions is even. Whence "parity".

Historyfree (or positional) determinacy that is refered to in the definition is a mere property of parity games that was shown by Mostowski and independently Jutla and Emerson.

Are there conflicting notions in Game Theory that I am not aware of? Is there a source of the definition given in the article?

Christian.kissig 08:37, 2 April 2007 (UTC)