{"scopus_import":"1","date_created":"2025-04-06T22:01:32Z","title":"Random zero-sum dynamic games on infinite directed graphs","department":[{"_id":"MaKw"},{"_id":"KrCh"}],"language":[{"iso":"eng"}],"date_updated":"2025-05-14T11:40:04Z","date_published":"2025-01-01T00:00:00Z","project":[{"name":"Formal Methods for Stochastic Models: Algorithms and Applications","call_identifier":"H2020","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","grant_number":"863818"}],"doi":"10.1007/s13235-025-00636-4","_id":"19508","author":[{"first_name":"Luc","full_name":"Attia, Luc","last_name":"Attia"},{"id":"9aa8388e-d003-11ee-8458-c4c1d7447977","last_name":"Lichev","first_name":"Lyuben","full_name":"Lichev, Lyuben"},{"full_name":"Mitsche, Dieter","first_name":"Dieter","last_name":"Mitsche"},{"orcid":"0000-0001-5103-038X","last_name":"Saona Urmeneta","id":"BD1DF4C4-D767-11E9-B658-BC13E6697425","full_name":"Saona Urmeneta, Raimundo J","first_name":"Raimundo J"},{"first_name":"Bruno","full_name":"Ziliotto, Bruno","last_name":"Ziliotto"}],"oa":1,"citation":{"ieee":"L. Attia, L. Lichev, D. Mitsche, R. J. Saona Urmeneta, and B. Ziliotto, “Random zero-sum dynamic games on infinite directed graphs,” <i>Dynamic Games and Applications</i>. Springer Nature, 2025.","short":"L. Attia, L. Lichev, D. Mitsche, R.J. Saona Urmeneta, B. Ziliotto, Dynamic Games and Applications (2025).","chicago":"Attia, Luc, Lyuben Lichev, Dieter Mitsche, Raimundo J Saona Urmeneta, and Bruno Ziliotto. “Random Zero-Sum Dynamic Games on Infinite Directed Graphs.” <i>Dynamic Games and Applications</i>. Springer Nature, 2025. <a href=\"https://doi.org/10.1007/s13235-025-00636-4\">https://doi.org/10.1007/s13235-025-00636-4</a>.","ama":"Attia L, Lichev L, Mitsche D, Saona Urmeneta RJ, Ziliotto B. Random zero-sum dynamic games on infinite directed graphs. <i>Dynamic Games and Applications</i>. 2025. doi:<a href=\"https://doi.org/10.1007/s13235-025-00636-4\">10.1007/s13235-025-00636-4</a>","apa":"Attia, L., Lichev, L., Mitsche, D., Saona Urmeneta, R. J., &#38; Ziliotto, B. (2025). Random zero-sum dynamic games on infinite directed graphs. <i>Dynamic Games and Applications</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s13235-025-00636-4\">https://doi.org/10.1007/s13235-025-00636-4</a>","mla":"Attia, Luc, et al. “Random Zero-Sum Dynamic Games on Infinite Directed Graphs.” <i>Dynamic Games and Applications</i>, Springer Nature, 2025, doi:<a href=\"https://doi.org/10.1007/s13235-025-00636-4\">10.1007/s13235-025-00636-4</a>.","ista":"Attia L, Lichev L, Mitsche D, Saona Urmeneta RJ, Ziliotto B. 2025. Random zero-sum dynamic games on infinite directed graphs. Dynamic Games and Applications."},"abstract":[{"lang":"eng","text":"We consider random two-player zero-sum dynamic games with perfect information on a class of infinite directed graphs. Starting from a fixed vertex, the players take turns to move a token along the edges of the graph. Every vertex is assigned a payoff known in advance by both players. Every time the token visits a vertex, Player 2 pays Player 1 the corresponding payoff. We consider a distribution over such games by assigning i.i.d. payoffs to the vertices. On the one hand, for acyclic directed graphs of bounded degree and sub-exponential expansion, we show that, when the duration of the game tends to infinity, the value converges almost surely to a constant at an exponential rate dominated in terms of the expansion. On 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."}],"oa_version":"Published Version","article_type":"original","publication":"Dynamic Games and Applications","article_processing_charge":"Yes (via OA deal)","publisher":"Springer Nature","corr_author":"1","month":"01","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). 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), by Fondecyt grant 1220174, by ANID Chile grant ACT210005, and by the ERC CoG 863818 (ForM-SMArt) grant. 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, under the IRL program of CNRS. This work was supported by Fondation CFM pour la Recherche. This paper has also been funded by the Agence Nationale de la Recherche under grant ANR-17-EURE-0010 (Investissements d’Avenir program).","ec_funded":1,"quality_controlled":"1","publication_identifier":{"eissn":["2153-0793"],"issn":["2153-0785"]},"status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_status":"epub_ahead","OA_place":"publisher","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1007/s13235-025-00636-4"}],"day":"01","OA_type":"hybrid","year":"2025","type":"journal_article"}