{"month":"07","type":"technical_report","publisher":"IST Austria","year":"2013","day":"03","publication_identifier":{"issn":["2664-1690"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","has_accepted_license":"1","oa":1,"oa_version":"Published Version","language":[{"iso":"eng"}],"date_created":"2018-12-12T11:39:08Z","date_published":"2013-07-03T00:00:00Z","file_date_updated":"2020-07-14T12:46:45Z","publication_status":"published","title":"Qualitative analysis of concurrent mean-payoff games","status":"public","pubrep_id":"126","ddc":["000","005"],"author":[{"first_name":"Krishnendu","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4561-241X","full_name":"Chatterjee, Krishnendu","last_name":"Chatterjee"},{"first_name":"Rasmus","id":"3B699956-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-4783-0389","full_name":"Ibsen-Jensen, Rasmus","last_name":"Ibsen-Jensen"}],"citation":{"ieee":"K. Chatterjee and R. Ibsen-Jensen, <i>Qualitative analysis of concurrent mean-payoff games</i>. IST Austria, 2013.","apa":"Chatterjee, K., &#38; Ibsen-Jensen, R. (2013). <i>Qualitative analysis of concurrent mean-payoff games</i>. IST Austria. <a href=\"https://doi.org/10.15479/AT:IST-2013-126-v1-1\">https://doi.org/10.15479/AT:IST-2013-126-v1-1</a>","mla":"Chatterjee, Krishnendu, and Rasmus Ibsen-Jensen. <i>Qualitative Analysis of Concurrent Mean-Payoff Games</i>. IST Austria, 2013, doi:<a href=\"https://doi.org/10.15479/AT:IST-2013-126-v1-1\">10.15479/AT:IST-2013-126-v1-1</a>.","chicago":"Chatterjee, Krishnendu, and Rasmus Ibsen-Jensen. <i>Qualitative Analysis of Concurrent Mean-Payoff Games</i>. IST Austria, 2013. <a href=\"https://doi.org/10.15479/AT:IST-2013-126-v1-1\">https://doi.org/10.15479/AT:IST-2013-126-v1-1</a>.","short":"K. Chatterjee, R. Ibsen-Jensen, Qualitative Analysis of Concurrent Mean-Payoff Games, IST Austria, 2013.","ama":"Chatterjee K, Ibsen-Jensen R. <i>Qualitative Analysis of Concurrent Mean-Payoff Games</i>. IST Austria; 2013. doi:<a href=\"https://doi.org/10.15479/AT:IST-2013-126-v1-1\">10.15479/AT:IST-2013-126-v1-1</a>","ista":"Chatterjee K, Ibsen-Jensen R. 2013. Qualitative analysis of concurrent mean-payoff games, IST Austria, 33p."},"doi":"10.15479/AT:IST-2013-126-v1-1","department":[{"_id":"KrCh"}],"alternative_title":["IST Austria Technical Report"],"file":[{"content_type":"application/pdf","date_created":"2018-12-12T11:53:49Z","file_size":434523,"access_level":"open_access","file_name":"IST-2013-126-v1+1_soda_full.pdf","creator":"system","date_updated":"2020-07-14T12:46:45Z","checksum":"063868c665beec37bf28160e2a695746","relation":"main_file","file_id":"5510"}],"page":"33","date_updated":"2023-02-23T12:22:53Z","related_material":{"record":[{"relation":"later_version","status":"public","id":"524"}]},"_id":"5403","abstract":[{"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 every 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 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 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 mean-payoff games) that is not known to be in polynomial time.","lang":"eng"}]}