{"language":[{"iso":"eng"}],"date_updated":"2023-02-23T12:23:40Z","publist_id":"3287","type":"preprint","publication":"arXiv","publication_status":"published","oa_version":"Preprint","abstract":[{"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.","lang":"eng"}],"_id":"3338","main_file_link":[{"url":"http://arxiv.org/abs/1107.2146","open_access":"1"}],"author":[{"full_name":"Chatterjee, Krishnendu","first_name":"Krishnendu","orcid":"0000-0002-4561-241X","last_name":"Chatterjee","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87"}],"related_material":{"record":[{"status":"public","id":"5380","relation":"earlier_version"}]},"title":"Bounded rationality in concurrent parity games","citation":{"mla":"Chatterjee, Krishnendu. “Bounded Rationality in Concurrent Parity Games.” <i>ArXiv</i>, ArXiv, 2011, pp. 1–51.","ama":"Chatterjee K. Bounded rationality in concurrent parity games. <i>arXiv</i>. 2011:1-51.","short":"K. Chatterjee, ArXiv (2011) 1–51.","ieee":"K. Chatterjee, “Bounded rationality in concurrent parity games,” <i>arXiv</i>. ArXiv, pp. 1–51, 2011.","ista":"Chatterjee K. 2011. Bounded rationality in concurrent parity games. arXiv, 1–51, .","chicago":"Chatterjee, Krishnendu. “Bounded Rationality in Concurrent Parity Games.” <i>ArXiv</i>. ArXiv, 2011.","apa":"Chatterjee, K. (2011). Bounded rationality in concurrent parity games. <i>arXiv</i>. ArXiv."},"month":"07","date_created":"2018-12-11T12:02:45Z","department":[{"_id":"KrCh"}],"date_published":"2011-07-11T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"year":"2011","publisher":"ArXiv","status":"public","page":"1 - 51","day":"11","external_id":{"arxiv":["1107.2146"]}}