{"year":"2024","day":"29","article_processing_charge":"No","date_published":"2024-01-29T00:00:00Z","publication":"arXiv","article_number":"2401.16252","date_updated":"2024-06-03T07:50:29Z","abstract":[{"lang":"eng","text":"This paper considers a class of two-player zero-sum games on directed graphs whose vertices are equipped with random payoffs of bounded support known by both players.\r\nStarting from a fixed vertex, players take turns to move a token along the edges of the graph.\r\nOn the one hand, for acyclic directed graphs of bounded degree and sub-exponential expansion, we show that the value of the game converges almost surely to a constant at an exponential rate dominated in terms of the expansion.\r\nOn the other hand, for the infinite d-ary tree that does not fall into the previous class of graphs, we show convergence at a double-exponential rate in terms of the expansion."}],"status":"public","date_created":"2024-06-03T07:45:22Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2401.16252"}],"department":[{"_id":"KrCh"}],"acknowledgement":"This work was supported by the French Agence Nationale de la Recherche (ANR) under references ANR-21-CE40-0020 (CONVERGENCE project) and ANR-20-CE40-0002 (GrHyDy), and by Fondecyt grant 1220174. This collaboration was mainly conducted during a 1-year visit of Bruno Ziliotto to the Center for Mathematical Modeling (CMM) at University of Chile in 2023,\r\nunder the IRL program of CNRS.","language":[{"iso":"eng"}],"author":[{"last_name":"Attia","first_name":"Luc","full_name":"Attia, Luc"},{"first_name":"Lyuben","full_name":"Lichev, Lyuben","last_name":"Lichev"},{"full_name":"Mitsche, Dieter","first_name":"Dieter","last_name":"Mitsche"},{"full_name":"Saona Urmeneta, Raimundo J","first_name":"Raimundo J","orcid":"0000-0001-5103-038X","id":"BD1DF4C4-D767-11E9-B658-BC13E6697425","last_name":"Saona Urmeneta"},{"last_name":"Ziliotto","full_name":"Ziliotto, Bruno","first_name":"Bruno"}],"publication_status":"submitted","oa":1,"oa_version":"Preprint","citation":{"chicago":"Attia, Luc, Lyuben Lichev, Dieter Mitsche, Raimundo J Saona Urmeneta, and Bruno Ziliotto. “Zero-Sum Random Games on Directed Graphs.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2401.16252\">https://doi.org/10.48550/arXiv.2401.16252</a>.","ieee":"L. Attia, L. Lichev, D. Mitsche, R. J. Saona Urmeneta, and B. Ziliotto, “Zero-sum random games on directed graphs,” <i>arXiv</i>. .","mla":"Attia, Luc, et al. “Zero-Sum Random Games on Directed Graphs.” <i>ArXiv</i>, 2401.16252, doi:<a href=\"https://doi.org/10.48550/arXiv.2401.16252\">10.48550/arXiv.2401.16252</a>.","ista":"Attia L, Lichev L, Mitsche D, Saona Urmeneta RJ, Ziliotto B. Zero-sum random games on directed graphs. arXiv, 2401.16252.","ama":"Attia L, Lichev L, Mitsche D, Saona Urmeneta RJ, Ziliotto B. Zero-sum random games on directed graphs. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2401.16252\">10.48550/arXiv.2401.16252</a>","apa":"Attia, L., Lichev, L., Mitsche, D., Saona Urmeneta, R. J., &#38; Ziliotto, B. (n.d.). Zero-sum random games on directed graphs. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2401.16252\">https://doi.org/10.48550/arXiv.2401.16252</a>","short":"L. Attia, L. Lichev, D. Mitsche, R.J. Saona Urmeneta, B. Ziliotto, ArXiv (n.d.)."},"type":"preprint","_id":"17101","doi":"10.48550/arXiv.2401.16252","external_id":{"arxiv":["2401.16252"]},"title":"Zero-sum random games on directed graphs","month":"01"}