{"id":{"repo_id":"passau-thes","oai_identifier":"oai:kobv.de-opus4-uni-passau:1968"},"canonical_url":"https://search.dev.ndltd.org/etd/passau-thes/oai:kobv.de-opus4-uni-passau:1968","repository":{"repo_id":"passau-thes","name":"Universität Passau","base_url":"https://opus4.kobv.de/opus4-uni-passau/oai"},"display":{"title":"Multi-Leader Congestion Games with an Adversary","abstract":"In this thesis, we introduced a congestion game with multiple leaders and a single follower (adversary) which is motivated by security applications with congestion effects. Our objective was to understand the result and the impact of selfish acting individuals in these games. In this regard, we analyzed the existence, the computation and the quality of (approximate) pure Nash equilibria. First, we observed that an exact pure Nash equilibrium always exists in the resulting strategic game among the leaders if the resource cost coefficients are identical and the underlying congestion game is a matroid congestion game. If one of these two conditions is not fulfilled, the existence of PNE is not ensured anymore in general. Consequently, we focused on approximate equilibria. For the case of symmetric singleton strategies, one of our main result established that K ≈ 1.1974, the unique solution of a cubic polynomial equation, is the smallest possible factor such that the existence of a K-approximate equilibrium is guaranteed for all instances of the game. To this end, we presented an efficient algorithm which computes a K-approximate PNE. Furthermore, we showed that the factor K is tight by providing an instance where no α-approximate PNE with α < K exists. However, for a specific symmetric singleton instance there might be a better α-approximate PNE, i.e., with α < K. A given instance could even admit an exact PNE. We provided therefore a polynomial time procedure that computes a best approximate PNE of a given instance. In particular, this procedure can verify the existence of an exact PNE in a given instance efficiently and, if it exists, can also determine the corresponding load vector. Finally, for symmetric singleton instances with two resources, we compared the total cost of a best (cheapest) and worst (most expensive) PNE to the total cost of an optimal outcome, termed by the price of stability and the price of anarchy, respectively. In particular, we verified that the PoS and the PoA are 4/3.","abstract_html":"In this thesis, we introduced a congestion game with multiple leaders and a single follower (adversary) which is motivated by security applications with congestion effects. Our objective was to understand the result and the impact of selfish acting individuals in these games. In this regard, we analyzed the existence, the computation and the quality of (approximate) pure Nash equilibria. First, we observed that an exact pure Nash equilibrium always exists in the resulting strategic game among the leaders if the resource cost coefficients are identical and the underlying congestion game is a matroid congestion game. If one of these two conditions is not fulfilled, the existence of PNE is not ensured anymore in general. Consequently, we focused on approximate equilibria. For the case of symmetric singleton strategies, one of our main result established that K ≈ 1.1974, the unique solution of a cubic polynomial equation, is the smallest possible factor such that the existence of a K-approximate equilibrium is guaranteed for all instances of the game. To this end, we presented an efficient algorithm which computes a K-approximate PNE. Furthermore, we showed that the factor K is tight by providing an instance where no α-approximate PNE with α &lt; K exists. However, for a specific symmetric singleton instance there might be a better α-approximate PNE, i.e., with α &lt; K. A given instance could even admit an exact PNE. We provided therefore a polynomial time procedure that computes a best approximate PNE of a given instance. In particular, this procedure can verify the existence of an exact PNE in a given instance efficiently and, if it exists, can also determine the corresponding load vector. Finally, for symmetric singleton instances with two resources, we compared the total cost of a best (cheapest) and worst (most expensive) PNE to the total cost of an optimal outcome, termed by the price of stability and the price of anarchy, respectively. In particular, we verified that the PoS and the PoA are 4/3.","abstract_has_math":false,"creators":["Henle, Mona"],"institution":"Universität Passau","degree_name":null,"degree_level":"thesis.doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":["Harks, Tobias","Klimm, Max","Peis, Britta"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2025,"date_issued":"2025-07-21","date_published":"2025-07-21","updated_at":"2026-07-24T03:45:12Z","subjects":["Congestion Games","Game Theory","Adversary"],"languages":[],"rights":["Creative Commons - CC BY - Namensnennung 4.0 International"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://opus4.kobv.de/opus4-uni-passau/frontdoor/index/index/docId/1968","outbound_label":"Repository record","outbound_source":"source_url"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Harks, Tobias","Klimm, Max","Peis, Britta"]},{"key":"dc:creator","label":"Author","values":["Henle, Mona"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:publisher","label":"Institution","values":["Universität Passau"]},{"key":"dc:type","label":"Dc Type","values":["doctoralThesis"]},{"key":"thesis:degree_level","label":"Degree Level","values":["thesis.doctoral"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Universität Passau"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Congestion Games","Game Theory","Adversary"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["Creative Commons - CC BY - Namensnennung 4.0 International"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this thesis, we introduced a congestion game with multiple leaders and a single follower (adversary) which is motivated by security applications with congestion effects. Our objective was to understand the result and the impact of selfish acting individuals in these games. In this regard, we analyzed the existence, the computation and the quality of (approximate) pure Nash equilibria. First, we observed that an exact pure Nash equilibrium always exists in the resulting strategic game among the leaders if the resource cost coefficients are identical and the underlying congestion game is a matroid congestion game. If one of these two conditions is not fulfilled, the existence of PNE is not ensured anymore in general. Consequently, we focused on approximate equilibria. For the case of symmetric singleton strategies, one of our main result established that K ≈ 1.1974, the unique solution of a cubic polynomial equation, is the smallest possible factor such that the existence of a K-approximate equilibrium is guaranteed for all instances of the game. To this end, we presented an efficient algorithm which computes a K-approximate PNE. Furthermore, we showed that the factor K is tight by providing an instance where no α-approximate PNE with α < K exists. However, for a specific symmetric singleton instance there might be a better α-approximate PNE, i.e., with α < K. A given instance could even admit an exact PNE. We provided therefore a polynomial time procedure that computes a best approximate PNE of a given instance. In particular, this procedure can verify the existence of an exact PNE in a given instance efficiently and, if it exists, can also determine the corresponding load vector. Finally, for symmetric singleton instances with two resources, we compared the total cost of a best (cheapest) and worst (most expensive) PNE to the total cost of an optimal outcome, termed by the price of stability and the price of anarchy, respectively. In particular, we verified that the PoS and the PoA are 4/3."]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Multi-Leader Congestion Games with an Adversary"]}]}],"canonical_facts":{"dc:contributor":["Harks, Tobias","Klimm, Max","Peis, Britta"],"dc:creator":["Henle, Mona"],"dc:description.abstract":["In this thesis, we introduced a congestion game with multiple leaders and a single follower (adversary) which is motivated by security applications with congestion effects. Our objective was to understand the result and the impact of selfish acting individuals in these games. In this regard, we analyzed the existence, the computation and the quality of (approximate) pure Nash equilibria. First, we observed that an exact pure Nash equilibrium always exists in the resulting strategic game among the leaders if the resource cost coefficients are identical and the underlying congestion game is a matroid congestion game. If one of these two conditions is not fulfilled, the existence of PNE is not ensured anymore in general. Consequently, we focused on approximate equilibria. For the case of symmetric singleton strategies, one of our main result established that K ≈ 1.1974, the unique solution of a cubic polynomial equation, is the smallest possible factor such that the existence of a K-approximate equilibrium is guaranteed for all instances of the game. To this end, we presented an efficient algorithm which computes a K-approximate PNE. Furthermore, we showed that the factor K is tight by providing an instance where no α-approximate PNE with α < K exists. However, for a specific symmetric singleton instance there might be a better α-approximate PNE, i.e., with α < K. A given instance could even admit an exact PNE. We provided therefore a polynomial time procedure that computes a best approximate PNE of a given instance. In particular, this procedure can verify the existence of an exact PNE in a given instance efficiently and, if it exists, can also determine the corresponding load vector. Finally, for symmetric singleton instances with two resources, we compared the total cost of a best (cheapest) and worst (most expensive) PNE to the total cost of an optimal outcome, termed by the price of stability and the price of anarchy, respectively. In particular, we verified that the PoS and the PoA are 4/3."],"dc:format.medium":["application/pdf"],"dc:publisher":["Universität Passau"],"dc:rights":["Creative Commons - CC BY - Namensnennung 4.0 International"],"dc:subject":["Congestion Games","Game Theory","Adversary"],"dc:title":["Multi-Leader Congestion Games with an Adversary"],"dc:type":["doctoralThesis"],"thesis:degree_level":["thesis.doctoral"],"thesis:institution_name":["Universität Passau"]},"updated_at":"2026-07-24T03:45:12Z"}