{"year":"2013","page":"29","day":"03","date_created":"2018-12-12T11:39:08Z","ddc":["000","005"],"language":[{"iso":"eng"}],"doi":"10.15479/AT:IST-2013-127-v1-1","has_accepted_license":"1","oa":1,"status":"public","publication_identifier":{"issn":["2664-1690"]},"title":"The complexity of ergodic games","date_published":"2013-07-03T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","pubrep_id":"127","publication_status":"published","date_updated":"2023-02-23T10:30:55Z","abstract":[{"lang":"eng","text":"We study finite-state two-player (zero-sum) concurrent mean-payoff games played on a graph. We focus on the important sub-class of ergodic games where all states are visited infinitely often with probability 1. The algorithmic study of ergodic games was initiated in a seminal work of Hoffman and Karp in 1966, but all basic complexity questions have remained unresolved. Our main results for ergodic games are as follows: We establish (1) an optimal exponential bound 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); (2) the approximation problem lie in FNP; (3) the approximation problem is at least as hard as the decision problem for simple stochastic games (for which NP and coNP is the long-standing best known bound). We show that the exact value can be expressed in the existential theory of the reals, and also establish square-root sum hardness for a related class of games."}],"publisher":"IST Austria","citation":{"ieee":"K. Chatterjee and R. Ibsen-Jensen, <i>The complexity of ergodic games</i>. IST Austria, 2013.","ama":"Chatterjee K, Ibsen-Jensen R. <i>The Complexity of Ergodic Games</i>. IST Austria; 2013. doi:<a href=\"https://doi.org/10.15479/AT:IST-2013-127-v1-1\">10.15479/AT:IST-2013-127-v1-1</a>","ista":"Chatterjee K, Ibsen-Jensen R. 2013. The complexity of ergodic games, IST Austria, 29p.","short":"K. Chatterjee, R. Ibsen-Jensen, The Complexity of Ergodic Games, IST Austria, 2013.","mla":"Chatterjee, Krishnendu, and Rasmus Ibsen-Jensen. <i>The Complexity of Ergodic Games</i>. IST Austria, 2013, doi:<a href=\"https://doi.org/10.15479/AT:IST-2013-127-v1-1\">10.15479/AT:IST-2013-127-v1-1</a>.","apa":"Chatterjee, K., &#38; Ibsen-Jensen, R. (2013). <i>The complexity of ergodic games</i>. IST Austria. <a href=\"https://doi.org/10.15479/AT:IST-2013-127-v1-1\">https://doi.org/10.15479/AT:IST-2013-127-v1-1</a>","chicago":"Chatterjee, Krishnendu, and Rasmus Ibsen-Jensen. <i>The Complexity of Ergodic Games</i>. IST Austria, 2013. <a href=\"https://doi.org/10.15479/AT:IST-2013-127-v1-1\">https://doi.org/10.15479/AT:IST-2013-127-v1-1</a>."},"author":[{"first_name":"Krishnendu","orcid":"0000-0002-4561-241X","last_name":"Chatterjee","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","full_name":"Chatterjee, Krishnendu"},{"orcid":"0000-0003-4783-0389","id":"3B699956-F248-11E8-B48F-1D18A9856A87","last_name":"Ibsen-Jensen","first_name":"Rasmus","full_name":"Ibsen-Jensen, Rasmus"}],"related_material":{"record":[{"id":"2162","status":"public","relation":"later_version"}]},"month":"07","oa_version":"Published Version","file":[{"creator":"system","file_id":"5496","checksum":"79ee5e677a82611ce06e0360c69d494a","date_updated":"2020-07-14T12:46:45Z","file_size":517275,"file_name":"IST-2013-127-v1+1_ergodic.pdf","relation":"main_file","access_level":"open_access","date_created":"2018-12-12T11:53:35Z","content_type":"application/pdf"}],"file_date_updated":"2020-07-14T12:46:45Z","_id":"5404","type":"technical_report","department":[{"_id":"KrCh"}],"alternative_title":["IST Austria Technical Report"]}