Talk:Parity game

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)

Note

That we need to link to Rabin's tree theorem or something like that once it's written. Tijfo098 (talk) 03:35, 15 November 2012 (UTC)

Recent quasipolynomial time algorithms

There seems to be a consensus now that Parity Games can be solved in quasipolynomial time. See for example the references listed here:

• Deciding Parity Games in Quasipolynomial Time (PDF), by Cristian S. Calude, Sanjay Jain, Bakhadyr Khoussainov, Wei Li, and Frank Stephan.
• A short proof of correctness of the quasi-polynomial time algorithm for parity games, by Hugo Gimbert and Rasmus Ibsen-Jensen.
• Succinct progress measures for solving parity games, by Marcin Jurdziński and Ranko Lazić.

An implementation and comparison with previous approaches is available (classic strategy improvement "wins" on random instances, but gets "slow" on Friedmann’s trap examples):

• An Ordered Approach to Solving Parity Games in Quasi Polynomial Time and Quasi Linear Space, by John Fearnley, Sanjay Jain, Sven Schewe, Frank Stephan, Dominik Wojtczak

Jakito (talk) 01:49, 13 March 2017 (UTC)