---
_id: '3338'
abstract:
- lang: eng
text: 'We consider 2-player games played on a finite state space for an infinite
number of rounds. The games are concurrent: in each round, the two players (player
1 and player 2) choose their moves inde- pendently and simultaneously; the current
state and the two moves determine the successor state. We study concurrent games
with ω-regular winning conditions specified as parity objectives. We consider
the qualitative analysis problems: the computation of the almost-sure and limit-sure
winning set of states, where player 1 can ensure to win with probability 1 and
with probability arbitrarily close to 1, respec- tively. In general the almost-sure
and limit-sure winning strategies require both infinite-memory as well as infinite-precision
(to describe probabilities). We study the bounded-rationality problem for qualitative
analysis of concurrent parity games, where the strategy set for player 1 is restricted
to bounded-resource strategies. In terms of precision, strategies can be deterministic,
uniform, finite-precision or infinite- precision; and in terms of memory, strategies
can be memoryless, finite-memory or infinite-memory. We present a precise and
complete characterization of the qualitative winning sets for all combinations
of classes of strategies. In particular, we show that uniform memoryless strategies
are as powerful as finite-precision infinite-memory strategies, and infinite-precision
memoryless strategies are as power- ful as infinite-precision finite-memory strategies.
We show that the winning sets can be computed in O(n2d+3) time, where n is the
size of the game structure and 2d is the number of priorities (or colors), and
our algorithms are symbolic. The membership problem of whether a state belongs
to a winning set can be decided in NP ∩ coNP. While this complexity is the same
as for the simpler class of turn-based parity games, where in each state only
one of the two players has a choice of moves, our algorithms, that are obtained
by characterization of the winning sets as μ-calculus formulas, are considerably
more involved than those for turn-based games.'
author:
- first_name: Krishnendu
full_name: Chatterjee, Krishnendu
id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
last_name: Chatterjee
orcid: 0000-0002-4561-241X
citation:
ama: Chatterjee K. Bounded rationality in concurrent parity games. arXiv.
2011:1-51.
apa: Chatterjee, K. (2011). Bounded rationality in concurrent parity games. arXiv.
ArXiv.
chicago: Chatterjee, Krishnendu. “Bounded Rationality in Concurrent Parity Games.”
ArXiv. ArXiv, 2011.
ieee: K. Chatterjee, “Bounded rationality in concurrent parity games,” arXiv.
ArXiv, pp. 1–51, 2011.
ista: Chatterjee K. 2011. Bounded rationality in concurrent parity games. arXiv,
1–51, .
mla: Chatterjee, Krishnendu. “Bounded Rationality in Concurrent Parity Games.” ArXiv,
ArXiv, 2011, pp. 1–51.
short: K. Chatterjee, ArXiv (2011) 1–51.
date_created: 2018-12-11T12:02:45Z
date_published: 2011-07-11T00:00:00Z
date_updated: 2023-02-23T12:23:40Z
day: '11'
department:
- _id: KrCh
external_id:
arxiv:
- '1107.2146'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1107.2146
month: '07'
oa: 1
oa_version: Preprint
page: 1 - 51
publication: arXiv
publication_status: published
publisher: ArXiv
publist_id: '3287'
related_material:
record:
- id: '5380'
relation: earlier_version
status: public
status: public
title: Bounded rationality in concurrent parity games
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2011'
...