{"date_published":"2015-10-11T00:00:00Z","year":"2015","publisher":"Elsevier","day":"11","intvolume":"       242","language":[{"iso":"eng"}],"publist_id":"7295","issue":"6","oa_version":"Preprint","main_file_link":[{"url":"https://arxiv.org/abs/1409.5306","open_access":"1"}],"title":"Qualitative analysis of concurrent mean payoff games","scopus_import":1,"quality_controlled":"1","citation":{"apa":"Chatterjee, K., &#38; Ibsen-Jensen, R. (2015). Qualitative analysis of concurrent mean payoff games. <i>Information and Computation</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.ic.2015.03.009\">https://doi.org/10.1016/j.ic.2015.03.009</a>","chicago":"Chatterjee, Krishnendu, and Rasmus Ibsen-Jensen. “Qualitative Analysis of Concurrent Mean Payoff Games.” <i>Information and Computation</i>. Elsevier, 2015. <a href=\"https://doi.org/10.1016/j.ic.2015.03.009\">https://doi.org/10.1016/j.ic.2015.03.009</a>.","ista":"Chatterjee K, Ibsen-Jensen R. 2015. Qualitative analysis of concurrent mean payoff games. Information and Computation. 242(6), 2–24.","ieee":"K. Chatterjee and R. Ibsen-Jensen, “Qualitative analysis of concurrent mean payoff games,” <i>Information and Computation</i>, vol. 242, no. 6. Elsevier, pp. 2–24, 2015.","short":"K. Chatterjee, R. Ibsen-Jensen, Information and Computation 242 (2015) 2–24.","mla":"Chatterjee, Krishnendu, and Rasmus Ibsen-Jensen. “Qualitative Analysis of Concurrent Mean Payoff Games.” <i>Information and Computation</i>, vol. 242, no. 6, Elsevier, 2015, pp. 2–24, doi:<a href=\"https://doi.org/10.1016/j.ic.2015.03.009\">10.1016/j.ic.2015.03.009</a>.","ama":"Chatterjee K, Ibsen-Jensen R. Qualitative analysis of concurrent mean payoff games. <i>Information and Computation</i>. 2015;242(6):2-24. doi:<a href=\"https://doi.org/10.1016/j.ic.2015.03.009\">10.1016/j.ic.2015.03.009</a>"},"date_created":"2018-12-11T11:46:57Z","month":"10","department":[{"_id":"KrCh"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"page":"2 - 24","status":"public","external_id":{"arxiv":["1409.5306"]},"volume":242,"date_updated":"2023-02-23T12:24:45Z","type":"journal_article","publication_status":"published","publication":"Information and Computation","abstract":[{"lang":"eng","text":"We consider concurrent games played by two players on a finite-state graph, where in every round the players simultaneously choose a move, and the current state along with the joint moves determine the successor state. We study the most fundamental objective for concurrent games, namely, mean-payoff or limit-average objective, where a reward is associated to each transition, and the goal of player 1 is to maximize the long-run average of the rewards, and the objective of player 2 is strictly the opposite (i.e., the games are zero-sum). The path constraint for player 1 could be qualitative, i.e., the mean-payoff is the maximal reward, or arbitrarily close to it; or quantitative, i.e., a given threshold between the minimal and maximal reward. We consider the computation of the almost-sure (resp. positive) winning sets, where player 1 can ensure that the path constraint is satisfied with probability 1 (resp. positive probability). Almost-sure winning with qualitative constraint exactly corresponds to the question of whether there exists a strategy to ensure that the payoff is the maximal reward of the game. Our main results for qualitative path constraints are as follows: (1) we establish qualitative determinacy results that show that for every state either player 1 has a strategy to ensure almost-sure (resp. positive) winning against all player-2 strategies, or player 2 has a spoiling strategy to falsify almost-sure (resp. positive) winning against all player-1 strategies; (2) we present optimal strategy complexity results that precisely characterize the classes of strategies required for almost-sure and positive winning for both players; and (3) we present quadratic time algorithms to compute the almost-sure and the positive winning sets, matching the best known bound of the algorithms for much simpler problems (such as reachability objectives). For quantitative constraints we show that a polynomial time solution for the almost-sure or the positive winning set would imply a solution to a long-standing open problem (of solving the value problem of turn-based deterministic mean-payoff games) that is not known to be solvable in polynomial time."}],"author":[{"orcid":"0000-0002-4561-241X","full_name":"Chatterjee, Krishnendu","first_name":"Krishnendu","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","last_name":"Chatterjee"},{"orcid":"0000-0003-4783-0389","full_name":"Ibsen-Jensen, Rasmus","first_name":"Rasmus","id":"3B699956-F248-11E8-B48F-1D18A9856A87","last_name":"Ibsen-Jensen"}],"doi":"10.1016/j.ic.2015.03.009","_id":"524","related_material":{"record":[{"relation":"earlier_version","status":"public","id":"5403"}]}}