{"abstract":[{"lang":"eng","text":"We consider concurrent mean-payoff games, a very well-studied class of two-player (player 1 vs player 2) zero-sum games on finite-state graphs where every transition is assigned a reward between 0 and 1, and the payoff function is the long-run average of the rewards. The value is the maximal expected payoff that player 1 can guarantee against all strategies of player 2. We consider the computation of the set of states with value 1 under finite-memory strategies for player 1, and our main results for the problem are as follows: (1) we present a polynomial-time algorithm; (2) we show that whenever there is a finite-memory strategy, there is a stationary strategy that does not need memory at all; and (3) we present an optimal bound (which is double exponential) on the patience of stationary strategies (where patience of a distribution is the inverse of the smallest positive probability and represents a complexity measure of a stationary strategy)."}],"publication_identifier":{"issn":["2664-1690"]},"ddc":["000","005"],"department":[{"_id":"KrCh"}],"alternative_title":["IST Austria Technical Report"],"publisher":"IST Austria","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file_date_updated":"2020-07-14T12:46:50Z","month":"04","has_accepted_license":"1","year":"2014","date_published":"2014-04-14T00:00:00Z","citation":{"ama":"Chatterjee K, Ibsen-Jensen R. <i>The Value 1 Problem for Concurrent Mean-Payoff Games</i>. IST Austria; 2014. doi:<a href=\"https://doi.org/10.15479/AT:IST-2014-191-v1-1\">10.15479/AT:IST-2014-191-v1-1</a>","chicago":"Chatterjee, Krishnendu, and Rasmus Ibsen-Jensen. <i>The Value 1 Problem for Concurrent Mean-Payoff Games</i>. IST Austria, 2014. <a href=\"https://doi.org/10.15479/AT:IST-2014-191-v1-1\">https://doi.org/10.15479/AT:IST-2014-191-v1-1</a>.","short":"K. Chatterjee, R. Ibsen-Jensen, The Value 1 Problem for Concurrent Mean-Payoff Games, IST Austria, 2014.","ista":"Chatterjee K, Ibsen-Jensen R. 2014. The value 1 problem for concurrent mean-payoff games, IST Austria, 49p.","ieee":"K. Chatterjee and R. Ibsen-Jensen, <i>The value 1 problem for concurrent mean-payoff games</i>. IST Austria, 2014.","apa":"Chatterjee, K., &#38; Ibsen-Jensen, R. (2014). <i>The value 1 problem for concurrent mean-payoff games</i>. IST Austria. <a href=\"https://doi.org/10.15479/AT:IST-2014-191-v1-1\">https://doi.org/10.15479/AT:IST-2014-191-v1-1</a>","mla":"Chatterjee, Krishnendu, and Rasmus Ibsen-Jensen. <i>The Value 1 Problem for Concurrent Mean-Payoff Games</i>. IST Austria, 2014, doi:<a href=\"https://doi.org/10.15479/AT:IST-2014-191-v1-1\">10.15479/AT:IST-2014-191-v1-1</a>."},"status":"public","publication_status":"published","_id":"5420","page":"49","type":"technical_report","oa_version":"Published Version","file":[{"checksum":"49e0fd3e62650346daf7dc04604f7a0a","access_level":"open_access","date_updated":"2020-07-14T12:46:50Z","file_name":"IST-2014-191-v1+1_main_full.pdf","creator":"system","relation":"main_file","content_type":"application/pdf","file_size":584368,"file_id":"5520","date_created":"2018-12-12T11:53:58Z"}],"day":"14","date_created":"2018-12-12T11:39:14Z","pubrep_id":"191","author":[{"full_name":"Chatterjee, Krishnendu","last_name":"Chatterjee","first_name":"Krishnendu","orcid":"0000-0002-4561-241X","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Ibsen-Jensen, Rasmus","last_name":"Ibsen-Jensen","orcid":"0000-0003-4783-0389","id":"3B699956-F248-11E8-B48F-1D18A9856A87","first_name":"Rasmus"}],"oa":1,"title":"The value 1 problem for concurrent mean-payoff games","doi":"10.15479/AT:IST-2014-191-v1-1","date_updated":"2021-01-12T08:02:05Z","language":[{"iso":"eng"}]}