{"license":"https://creativecommons.org/licenses/by-nc-sa/4.0/","file":[{"date_created":"2025-08-14T09:54:43Z","file_id":"20177","file_name":"2025_Svoboda_Jakub_Thesis.pdf","success":1,"content_type":"application/pdf","file_size":5927291,"date_updated":"2025-08-14T09:54:43Z","checksum":"c6c4df9777f4537940de7ab392ad57e2","creator":"jsvoboda","access_level":"open_access","relation":"main_file"},{"relation":"source_file","access_level":"closed","creator":"jsvoboda","date_updated":"2025-08-21T11:48:39Z","checksum":"485e9f9822821bc03666d245d80aaa08","file_size":6731815,"content_type":"application/zip","file_id":"20178","date_created":"2025-08-14T09:55:20Z","file_name":"2025_Svoboda_Jakub_Thesis.zip"}],"date_created":"2025-08-05T14:33:59Z","year":"2025","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","month":"08","doi":"10.15479/AT-ISTA-20138","article_processing_charge":"No","corr_author":"1","supervisor":[{"last_name":"Chatterjee","first_name":"Krishnendu","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","full_name":"Chatterjee, Krishnendu","orcid":"0000-0002-4561-241X"}],"publication_status":"published","ddc":["000","519"],"date_published":"2025-08-05T00:00:00Z","publisher":"Institute of Science and Technology Austria","file_date_updated":"2025-08-21T11:48:39Z","title":"Structural properties of games on graphs","publication_identifier":{"issn":["2663-337X"]},"degree_awarded":"PhD","citation":{"ista":"Svoboda J. 2025. Structural properties of games on graphs. Institute of Science and Technology Austria.","ieee":"J. Svoboda, “Structural properties of games on graphs,” Institute of Science and Technology Austria, 2025.","chicago":"Svoboda, Jakub. “Structural Properties of Games on Graphs.” Institute of Science and Technology Austria, 2025. <a href=\"https://doi.org/10.15479/AT-ISTA-20138\">https://doi.org/10.15479/AT-ISTA-20138</a>.","ama":"Svoboda J. Structural properties of games on graphs. 2025. doi:<a href=\"https://doi.org/10.15479/AT-ISTA-20138\">10.15479/AT-ISTA-20138</a>","short":"J. Svoboda, Structural Properties of Games on Graphs, Institute of Science and Technology Austria, 2025.","apa":"Svoboda, J. (2025). <i>Structural properties of games on graphs</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/AT-ISTA-20138\">https://doi.org/10.15479/AT-ISTA-20138</a>","mla":"Svoboda, Jakub. <i>Structural Properties of Games on Graphs</i>. Institute of Science and Technology Austria, 2025, doi:<a href=\"https://doi.org/10.15479/AT-ISTA-20138\">10.15479/AT-ISTA-20138</a>."},"day":"05","oa":1,"abstract":[{"lang":"eng","text":"The evolution shapes the world around us.\r\nNot only in biology, where the fittest individuals spread their genes but also in physics and social dynamics, the evolutionary forces determine the development of a state of matter or public opinions.\r\nMany models describe these dynamics.\r\nThis thesis examines the role of the structure in the models of selection.\r\nThe population structure is represented as a graph or a network, and each vertex is occupied by one individual.\r\nEvery individual has a type and fitness that represents the reproductive potential and depends on the type, occupied vertex, and the arrangement of the neighbors.\r\nThe evolution is modeled in discrete steps; in one step, one individual is replaced by a neighbor selected randomly with the influence of fitness.\r\n\r\n\r\n\r\nThe role of the networks is widely examined in the literature.\r\nThe structures that promote the spread of the desired type compared to the structureless case are called amplifiers.\r\nThe existence of amplifiers in various settings is an intensively studied topic, and in some settings, the amplifiers have been identified.\r\nMoreover, there are other important questions about the number of steps until one type spreads over the whole network (fixation time), the computational complexity, and the questions about the robustness of these processes.\r\n\r\n\r\nThis thesis explores the role of structure in evolution from many perspectives.\r\nFirst, it introduces different models and various choices that can be made in the models of evolution.\r\nIt highlights the role of the structure in the real world and how this is reflected in these models.\r\nThen, it describes the previous results and open problems.\r\nSecond, the thesis describes an amplifier for two variants of the Moran process: one with a constant birth rate and the other with a constant death rate.\r\nThis is an important contribution to the robustness of the amplification.\r\nThird, the thesis determines the complexity of spatial games.\r\nThese are processes where the fitness comes from a game, and the strength of selection is high.\r\nIt shows that determining the fate of cooperation in these games is a PSPACE-complete problem.\r\nFourth, the thesis describes the amplifier of cooperation for spatial games.\r\nThis is the first amplifier in this setting.\r\nFifth, the thesis examines the coexistence in the Moran process with environmental heterogeneity.\r\nIn this setting, the fitness depends not only on the type of the individual but also on the occupied vertex.\r\nThe chapter determines the relationship between the interactions of vertices of different types and the coexistence time.\r\nSixth, the thesis examines the social balance on networks and proposes a stochastic dynamic partially aware of the state of the graph, which reaches a balanced position quickly.\r\nFinally, the thesis presents conclusions and outlines the directions for future work.\r\n\r\n\r\n"}],"acknowledgement":"This work was supported by the European Research Council CoG 863818 (ForMSMArt) and Austrian Science Fund 10.55776/COE12.\r\n","related_material":{"record":[{"id":"15297","relation":"part_of_dissertation","status":"public"},{"id":"12787","relation":"part_of_dissertation","status":"public"},{"id":"12101","relation":"part_of_dissertation","status":"public"},{"status":"public","relation":"part_of_dissertation","id":"18703"},{"status":"public","relation":"part_of_dissertation","id":"12257"}]},"alternative_title":["ISTA Thesis"],"oa_version":"Published Version","type":"dissertation","ec_funded":1,"has_accepted_license":"1","author":[{"orcid":"0000-0002-1419-3267","id":"130759D2-D7DD-11E9-87D2-DE0DE6697425","full_name":"Svoboda, Jakub","first_name":"Jakub","last_name":"Svoboda"}],"page":"167","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode","image":"/images/cc_by_nc_sa.png","name":"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)","short":"CC BY-NC-SA (4.0)"},"_id":"20138","project":[{"grant_number":"863818","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","name":"Formal Methods for Stochastic Models: Algorithms and Applications","call_identifier":"H2020"}],"department":[{"_id":"GradSch"},{"_id":"KrCh"}],"OA_place":"repository","language":[{"iso":"eng"}],"status":"public","date_updated":"2025-08-21T12:50:13Z"}