---
_id: '475'
abstract:
- lang: eng
text: '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. '
alternative_title:
- EPTCS
author:
- first_name: Benjamin
full_name: Aminof, Benjamin
id: 4A55BD00-F248-11E8-B48F-1D18A9856A87
last_name: Aminof
- first_name: Sasha
full_name: Rubin, Sasha
id: 2EC51194-F248-11E8-B48F-1D18A9856A87
last_name: Rubin
citation:
ama: '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'
apa: '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'
chicago: 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.
ieee: B. Aminof and S. Rubin, “First cycle games,” in Electronic Proceedings
in Theoretical Computer Science, EPTCS, Grenoble, France, 2014, vol. 146,
pp. 83–90.
ista: 'Aminof B, Rubin S. 2014. First cycle games. Electronic Proceedings in Theoretical
Computer Science, EPTCS. SR: Strategic Reasoning, EPTCS, vol. 146, 83–90.'
mla: 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.
short: B. Aminof, S. Rubin, in:, Electronic Proceedings in Theoretical Computer
Science, EPTCS, Open Publishing Association, 2014, pp. 83–90.
conference:
end_date: 2014-04-06
location: Grenoble, France
name: 'SR: Strategic Reasoning'
start_date: 2014-04-05
date_created: 2018-12-11T11:46:41Z
date_published: 2014-04-01T00:00:00Z
date_updated: 2021-01-12T08:00:53Z
day: '01'
ddc:
- '004'
department:
- _id: KrCh
doi: 10.4204/EPTCS.146.11
ec_funded: 1
file:
- access_level: open_access
checksum: 4d7b4ab82980cca2b96ac7703992a8c8
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:17:08Z
date_updated: 2020-07-14T12:46:35Z
file_id: '5260'
file_name: IST-2018-952-v1+1_2014_Rubin_First_cycle.pdf
file_size: 100115
relation: main_file
file_date_updated: 2020-07-14T12:46:35Z
has_accepted_license: '1'
intvolume: ' 146'
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
page: 83 - 90
project:
- _id: 2584A770-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P 23499-N23
name: Modern Graph Algorithmic Techniques in Formal Verification
- _id: 25F5A88A-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: S11402-N23
name: Moderne Concurrency Paradigms
- _id: 25863FF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: S11407
name: Game Theory
- _id: 2581B60A-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '279307'
name: 'Quantitative Graph Games: Theory and Applications'
- _id: 25892FC0-B435-11E9-9278-68D0E5697425
grant_number: ICT15-003
name: Efficient Algorithms for Computer Aided Verification
publication: Electronic Proceedings in Theoretical Computer Science, EPTCS
publication_status: published
publisher: Open Publishing Association
publist_id: '7345'
pubrep_id: '952'
quality_controlled: '1'
scopus_import: 1
status: public
title: First cycle games
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: conference
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
volume: 146
year: '2014'
...