{"issue":"Part 2","publisher":"Springer","abstract":[{"lang":"eng","text":"We study two-player (zero-sum) concurrent mean-payoff games played on a finite-state 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 lies in FNP; (3) the approximation problem is at least as hard as the decision problem for simple stochastic games (for which NP ∩ coNP is the long-standing best known bound). We present a variant of the strategy-iteration algorithm by Hoffman and Karp; show that both our algorithm and the classical value-iteration algorithm can approximate the value in exponential time; and identify a subclass where the value-iteration algorithm is a FPTAS. We also show that the exact value can be expressed in the existential theory of the reals, and establish square-root sum hardness for a related class of games."}],"year":"2014","department":[{"_id":"KrCh"}],"oa_version":"Preprint","status":"public","ec_funded":1,"date_created":"2018-12-11T11:56:04Z","type":"conference","citation":{"chicago":"Chatterjee, Krishnendu, and Rasmus Ibsen-Jensen. “The Complexity of Ergodic Mean Payoff Games,” 8573:122–33. Springer, 2014. <a href=\"https://doi.org/10.1007/978-3-662-43951-7_11\">https://doi.org/10.1007/978-3-662-43951-7_11</a>.","apa":"Chatterjee, K., &#38; Ibsen-Jensen, R. (2014). The complexity of ergodic mean payoff games (Vol. 8573, pp. 122–133). Presented at the ICST: International Conference on Software Testing, Verification and Validation, Copenhagen, Denmark: Springer. <a href=\"https://doi.org/10.1007/978-3-662-43951-7_11\">https://doi.org/10.1007/978-3-662-43951-7_11</a>","ieee":"K. Chatterjee and R. Ibsen-Jensen, “The complexity of ergodic mean payoff games,” presented at the ICST: International Conference on Software Testing, Verification and Validation, Copenhagen, Denmark, 2014, vol. 8573, no. Part 2, pp. 122–133.","ama":"Chatterjee K, Ibsen-Jensen R. The complexity of ergodic mean payoff games. In: Vol 8573. Springer; 2014:122-133. doi:<a href=\"https://doi.org/10.1007/978-3-662-43951-7_11\">10.1007/978-3-662-43951-7_11</a>","ista":"Chatterjee K, Ibsen-Jensen R. 2014. The complexity of ergodic mean payoff games. ICST: International Conference on Software Testing, Verification and Validation, LNCS, vol. 8573, 122–133.","short":"K. Chatterjee, R. Ibsen-Jensen, in:, Springer, 2014, pp. 122–133.","mla":"Chatterjee, Krishnendu, and Rasmus Ibsen-Jensen. <i>The Complexity of Ergodic Mean Payoff Games</i>. Vol. 8573, no. Part 2, Springer, 2014, pp. 122–33, doi:<a href=\"https://doi.org/10.1007/978-3-662-43951-7_11\">10.1007/978-3-662-43951-7_11</a>."},"date_updated":"2023-02-23T12:24:48Z","month":"01","title":"The complexity of ergodic mean payoff games","publist_id":"4822","language":[{"iso":"eng"}],"quality_controlled":"1","intvolume":"      8573","related_material":{"record":[{"status":"public","id":"5404","relation":"earlier_version"}]},"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1404.5734"}],"oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","page":"122 - 133","day":"01","publication_status":"published","date_published":"2014-01-01T00:00:00Z","conference":{"location":"Copenhagen, Denmark","start_date":"2014-07-08","name":"ICST: International Conference on Software Testing, Verification and Validation","end_date":"2014-07-11"},"_id":"2162","alternative_title":["LNCS"],"volume":8573,"author":[{"first_name":"Krishnendu","full_name":"Chatterjee, Krishnendu","last_name":"Chatterjee","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4561-241X"},{"last_name":"Ibsen-Jensen","full_name":"Ibsen-Jensen, Rasmus","id":"3B699956-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-4783-0389","first_name":"Rasmus"}],"doi":"10.1007/978-3-662-43951-7_11","project":[{"name":"Modern Graph Algorithmic Techniques in Formal Verification","_id":"2584A770-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"P 23499-N23"},{"name":"Game Theory","_id":"25863FF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"S11407"},{"name":"Quantitative Graph Games: Theory and Applications","_id":"2581B60A-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"279307"},{"name":"Microsoft Research Faculty Fellowship","_id":"2587B514-B435-11E9-9278-68D0E5697425"}],"external_id":{"arxiv":["1404.5734"]}}