{"abstract":[{"text":"Game Theory is the mathematical formalization of social dynamics - systems where agents interact over time and the evolution of the state of the system depends on the decisions of every player. \r\nThis thesis takes the perspective of a single player and focuses on what they can guarantee in the worst case over the behavior of other players.\r\nIn other words, we consider that the objective of every other player in the game is exactly the opposite to the player.\r\nWe focus on sustained interactions over time, where the players repeatedly obtain quantitative rewards over time, and they are interested in maximizing their long-term performance.\t\r\nFormally, this thesis focuses on zero-sum games with the liminf average objective.\r\nTwo fundamental questions that Game Theory aims to answer are the following.\r\n\r\n1. How much can a player guarantee to obtain after the interaction?\r\n\r\n2. How to act in order to obtain the previously mentioned guarantee?\r\n\r\nThese questions are formalized by the concepts of \"value\" and \"optimal strategies\". \t\r\nWe study their properties on games that exhibit one or more of the following properties. \r\n\r\n1. Partial Observation: \r\nthe players can not perfectly observe the current state of the system during the game. We consider the model of (finite) Partially Observable Markov Decision Processes and prove that finite-memory strategies are sufficient to approximately guarantee the value.\r\n\r\n2. Perturbed Description: \r\nthe formal description of the game is perturbed by a small parameter.\r\nWe consider the model of (finite) Perturbed Matrix Games, and provide algorithms to check various robustness properties and to compute the parameterized value and optimal strategies.\r\n\r\n3. Stochastic Transitions: \r\nthe actions of the players determine the behavior of the evolution of the system, described as a probability distribution over the next state.\r\nWe consider the model of (finite) Perturbed Stochastic Games and provide formulas for the marginal value.\r\n\r\n4. Infinite States: \r\nthe system can be in infinitely many states.\r\nWe consider the model of Random Dynamic Games on a class of infinite graphs, prove the existence of the value, and quantify the concentration of finite-horizon values.","lang":"eng"}],"ec_funded":1,"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","publisher":"Institute of Science and Technology Austria","author":[{"first_name":"Raimundo J","id":"BD1DF4C4-D767-11E9-B658-BC13E6697425","full_name":"Saona Urmeneta, Raimundo J","orcid":"0000-0001-5103-038X","last_name":"Saona Urmeneta"}],"date_created":"2025-08-27T14:00:13Z","supervisor":[{"first_name":"Krishnendu","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","full_name":"Chatterjee, Krishnendu","orcid":"0000-0002-4561-241X","last_name":"Chatterjee"}],"corr_author":"1","has_accepted_license":"1","language":[{"iso":"eng"}],"file":[{"access_level":"open_access","creator":"rsaonaur","file_name":"2025_Saona_Raimundo_Thesis.pdf","file_id":"20240","date_created":"2025-08-28T14:47:07Z","success":1,"file_size":1503623,"date_updated":"2025-08-28T14:47:07Z","relation":"main_file","content_type":"application/pdf","checksum":"394a651f7de7085e509ef856ffe7bd97"},{"relation":"source_file","date_updated":"2025-08-28T14:47:12Z","checksum":"09fb2633e66aac80433d373f4180c5b4","content_type":"application/zip","file_id":"20241","file_name":"2025_Saona_Raimundo_Thesis.zip","creator":"rsaonaur","access_level":"closed","file_size":622747,"date_created":"2025-08-28T14:47:12Z"}],"type":"dissertation","oa_version":"Published Version","article_processing_charge":"No","date_updated":"2025-09-30T11:22:00Z","OA_place":"repository","title":"Robustness of solutions in game theory : Values and strategies in partially observable, perturbed, stochastic, and infinite games","degree_awarded":"PhD","month":"08","doi":"10.15479/AT-ISTA-20234","oa":1,"related_material":{"record":[{"status":"public","id":"9311","relation":"part_of_dissertation"},{"id":"17037","status":"public","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","status":"public","id":"18266"},{"status":"public","id":"19508","relation":"part_of_dissertation"}]},"publication_status":"published","day":"27","publication_identifier":{"issn":["2663-337X"]},"acknowledgement":"Funding sources The works included in this thesis were partially supported by:\r\n• Austrian Science Fund (FWF), grants 10.55776/COE12 and No RiSE/SHiNE S11407,\r\n• French Agence Nationale de la Recherche (ANR), grants ANR-21-CE40-0020 (CONVERGENCE) and ANR-20-CE40-0002 (GrHyDy),\r\n• Fondation Mathématique Jaques Hadamard, grant PGMO RSG 2018-0031H,\r\n• European Research Council (ERC), Consolidator grant 863818 (ForM-SMArt),\r\n• Agencia Nacional de Investigación y Desarrollo (ANID Chile), grant ACT210005,\r\n• Fondo Nacional de Desarrollo Científico y Tecnológico (Fondecyt Chile), grant 1220174,\r\n• Comisión Nacional de Investigación Científica y Tecnológica (CONICYT Chile), grant\r\nPII 20150140,\r\n• Evaluation-orientation de la Coopération Scientifique and Comisión Nacional de Investigación Científica y Tecnológica (ECOS-CONICYT), grant C15E03,\r\n• European Cooperation in Science and Technology (E-COST), grants CA16228 - European\r\nNetwork for Game Theory (GAMENET) and E-COST-GRANT-CA16228-c5a69859.\r\n","citation":{"ieee":"R. J. Saona Urmeneta, “Robustness of solutions in game theory : Values and strategies in partially observable, perturbed, stochastic, and infinite games,” Institute of Science and Technology Austria, 2025.","mla":"Saona Urmeneta, Raimundo J. <i>Robustness of Solutions in Game Theory : Values and Strategies in Partially Observable, Perturbed, Stochastic, and Infinite Games</i>. Institute of Science and Technology Austria, 2025, doi:<a href=\"https://doi.org/10.15479/AT-ISTA-20234\">10.15479/AT-ISTA-20234</a>.","chicago":"Saona Urmeneta, Raimundo J. “Robustness of Solutions in Game Theory : Values and Strategies in Partially Observable, Perturbed, Stochastic, and Infinite Games.” Institute of Science and Technology Austria, 2025. <a href=\"https://doi.org/10.15479/AT-ISTA-20234\">https://doi.org/10.15479/AT-ISTA-20234</a>.","short":"R.J. Saona Urmeneta, Robustness of Solutions in Game Theory : Values and Strategies in Partially Observable, Perturbed, Stochastic, and Infinite Games, Institute of Science and Technology Austria, 2025.","apa":"Saona Urmeneta, R. J. (2025). <i>Robustness of solutions in game theory : Values and strategies in partially observable, perturbed, stochastic, and infinite games</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/AT-ISTA-20234\">https://doi.org/10.15479/AT-ISTA-20234</a>","ista":"Saona Urmeneta RJ. 2025. Robustness of solutions in game theory : Values and strategies in partially observable, perturbed, stochastic, and infinite games. Institute of Science and Technology Austria.","ama":"Saona Urmeneta RJ. Robustness of solutions in game theory : Values and strategies in partially observable, perturbed, stochastic, and infinite games. 2025. doi:<a href=\"https://doi.org/10.15479/AT-ISTA-20234\">10.15479/AT-ISTA-20234</a>"},"page":"125","year":"2025","status":"public","ddc":["519"],"department":[{"_id":"GradSch"},{"_id":"KrCh"}],"date_published":"2025-08-27T00:00:00Z","project":[{"grant_number":"S11407","_id":"25863FF4-B435-11E9-9278-68D0E5697425","name":"Game Theory","call_identifier":"FWF"},{"call_identifier":"H2020","name":"Formal Methods for Stochastic Models: Algorithms and Applications","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","grant_number":"863818"}],"_id":"20234","file_date_updated":"2025-08-28T14:47:12Z","alternative_title":["ISTA Thesis"]}