First cycle games

B. Aminof, S. Rubin, in:, Electronic Proceedings in Theoretical Computer Science, EPTCS, Open Publishing Association, 2014, pp. 83–90.

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Conference Paper | Published | English
Department
Series Title
EPTCS
Abstract
First cycle games (FCG) are played on a finite graph by two players who push a token along the edges until a vertex is repeated, and a simple cycle is formed. The winner is determined by some fixed property Y of the sequence of labels of the edges (or nodes) forming this cycle. These games are traditionally of interest because of their connection with infinite-duration games such as parity and mean-payoff games. We study the memory requirements for winning strategies of FCGs and certain associated infinite duration games. We exhibit a simple FCG that is not memoryless determined (this corrects a mistake in Memoryless determinacy of parity and mean payoff games: a simple proof by Bj⋯orklund, Sandberg, Vorobyov (2004) that claims that FCGs for which Y is closed under cyclic permutations are memoryless determined). We show that θ (n)! memory (where n is the number of nodes in the graph), which is always sufficient, may be necessary to win some FCGs. On the other hand, we identify easy to check conditions on Y (i.e., Y is closed under cyclic permutations, and both Y and its complement are closed under concatenation) that are sufficient to ensure that the corresponding FCGs and their associated infinite duration games are memoryless determined. We demonstrate that many games considered in the literature, such as mean-payoff, parity, energy, etc., satisfy these conditions. On the complexity side, we show (for efficiently computable Y) that while solving FCGs is in PSPACE, solving some families of FCGs is PSPACE-hard.
Publishing Year
Date Published
2014-04-01
Proceedings Title
Electronic Proceedings in Theoretical Computer Science, EPTCS
Volume
146
Page
83 - 90
Conference
SR: Strategic Reasoning
Conference Location
Grenoble, France
Conference Date
2014-04-05 – 2014-04-06
IST-REx-ID

Cite this

Aminof B, Rubin S. First cycle games. In: Electronic Proceedings in Theoretical Computer Science, EPTCS. Vol 146. Open Publishing Association; 2014:83-90. doi:10.4204/EPTCS.146.11
Aminof, B., & Rubin, S. (2014). First cycle games. In Electronic Proceedings in Theoretical Computer Science, EPTCS (Vol. 146, pp. 83–90). Grenoble, France: Open Publishing Association. https://doi.org/10.4204/EPTCS.146.11
Aminof, Benjamin, and Sasha Rubin. “First Cycle Games.” In Electronic Proceedings in Theoretical Computer Science, EPTCS, 146:83–90. Open Publishing Association, 2014. https://doi.org/10.4204/EPTCS.146.11.
B. Aminof and S. Rubin, “First cycle games,” in Electronic Proceedings in Theoretical Computer Science, EPTCS, Grenoble, France, 2014, vol. 146, pp. 83–90.
Aminof B, Rubin S. 2014. First cycle games. Electronic Proceedings in Theoretical Computer Science, EPTCS. SR: Strategic Reasoning, EPTCS, vol. 146. 83–90.
Aminof, Benjamin, and Sasha Rubin. “First Cycle Games.” Electronic Proceedings in Theoretical Computer Science, EPTCS, vol. 146, Open Publishing Association, 2014, pp. 83–90, doi:10.4204/EPTCS.146.11.
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