{"day":"01","publisher":"Springer","year":"2016","ec_funded":1,"date_published":"2016-09-01T00:00:00Z","scopus_import":1,"quality_controlled":"1","title":"The big match in small space","main_file_link":[{"url":"https://arxiv.org/abs/1604.07634","open_access":"1"}],"oa_version":"Preprint","publist_id":"5927","language":[{"iso":"eng"}],"intvolume":"      9928","project":[{"call_identifier":"FWF","name":"Rigorous Systems Engineering","grant_number":"S 11407_N23","_id":"25832EC2-B435-11E9-9278-68D0E5697425"},{"grant_number":"ICT15-003","_id":"25892FC0-B435-11E9-9278-68D0E5697425","name":"Efficient Algorithms for Computer Aided Verification"},{"_id":"2581B60A-B435-11E9-9278-68D0E5697425","grant_number":"279307","call_identifier":"FP7","name":"Quantitative Graph Games: Theory and Applications"}],"status":"public","page":"64 - 76","oa":1,"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"KrCh"}],"month":"09","date_created":"2018-12-11T11:51:28Z","citation":{"chicago":"Hansen, Kristoffer, Rasmus Ibsen-Jensen, and Michal Koucký. “The Big Match in Small Space,” 9928:64–76. Springer, 2016. <a href=\"https://doi.org/10.1007/978-3-662-53354-3_6\">https://doi.org/10.1007/978-3-662-53354-3_6</a>.","ista":"Hansen K, Ibsen-Jensen R, Koucký M. 2016. The big match in small space. SAGT: Symposium on Algorithmic Game Theory, LNCS, vol. 9928, 64–76.","apa":"Hansen, K., Ibsen-Jensen, R., &#38; Koucký, M. (2016). The big match in small space (Vol. 9928, pp. 64–76). Presented at the SAGT: Symposium on Algorithmic Game Theory, Liverpool, United Kingdom: Springer. <a href=\"https://doi.org/10.1007/978-3-662-53354-3_6\">https://doi.org/10.1007/978-3-662-53354-3_6</a>","mla":"Hansen, Kristoffer, et al. <i>The Big Match in Small Space</i>. Vol. 9928, Springer, 2016, pp. 64–76, doi:<a href=\"https://doi.org/10.1007/978-3-662-53354-3_6\">10.1007/978-3-662-53354-3_6</a>.","ama":"Hansen K, Ibsen-Jensen R, Koucký M. The big match in small space. In: Vol 9928. Springer; 2016:64-76. doi:<a href=\"https://doi.org/10.1007/978-3-662-53354-3_6\">10.1007/978-3-662-53354-3_6</a>","short":"K. Hansen, R. Ibsen-Jensen, M. Koucký, in:, Springer, 2016, pp. 64–76.","ieee":"K. Hansen, R. Ibsen-Jensen, and M. Koucký, “The big match in small space,” presented at the SAGT: Symposium on Algorithmic Game Theory, Liverpool, United Kingdom, 2016, vol. 9928, pp. 64–76."},"alternative_title":["LNCS"],"_id":"1340","conference":{"name":"SAGT: Symposium on Algorithmic Game Theory","location":"Liverpool, United Kingdom","end_date":"2016-09-21","start_date":"2016-09-19"},"doi":"10.1007/978-3-662-53354-3_6","author":[{"last_name":"Hansen","first_name":"Kristoffer","full_name":"Hansen, Kristoffer"},{"last_name":"Ibsen-Jensen","id":"3B699956-F248-11E8-B48F-1D18A9856A87","full_name":"Ibsen-Jensen, Rasmus","first_name":"Rasmus","orcid":"0000-0003-4783-0389"},{"first_name":"Michal","full_name":"Koucký, Michal","last_name":"Koucký"}],"abstract":[{"lang":"eng","text":"We study repeated games with absorbing states, a type of two-player, zero-sum concurrent mean-payoff games with the prototypical example being the Big Match of Gillete (1957). These games may not allow optimal strategies but they always have ε-optimal strategies. In this paper we design ε-optimal strategies for Player 1 in these games that use only O(log log T) space. Furthermore, we construct strategies for Player 1 that use space s(T), for an arbitrary small unbounded non-decreasing function s, and which guarantee an ε-optimal value for Player 1 in the limit superior sense. The previously known strategies use space Ω(log T) and it was known that no strategy can use constant space if it is ε-optimal even in the limit superior sense. We also give a complementary lower bound. Furthermore, we also show that no Markov strategy, even extended with finite memory, can ensure value greater than 0 in the Big Match, answering a question posed by Neyman [11]."}],"publication_status":"published","type":"conference","date_updated":"2021-01-12T06:50:00Z","volume":9928}