eprintid: 4321 rev_number: 6 eprint_status: archive userid: 351 dir: disk0/00/00/43/21 datestamp: 2016-01-15 02:05:24 lastmod: 2021-08-27 17:35:59 status_changed: 2016-01-15 02:05:24 type: article metadata_visibility: show item_issues_count: 1 creators_name: Tarasyev, A.M. creators_id: 7340 title: The solution of evolutionary games using the theory of Hamilton-Jacobi equations ispublished: pub internal_subjects: iis_mod internal_subjects: iis_met internal_subjects: iis_ecl divisions: prog_dyn abstract: A dynamical model of a non-antagonistic evolutionary game for two coalitions is considered. The model features an infinite time span and discounted payoff functionals. A solution is presented using differential game theory. The solution is based on the construction of a value function for auxiliary antagonistic differential games and uses an approximate grid scheme from the theory of generalized solutions of the Hamilton-Jacobi equations. Together with the value functions the optimal guaranteeing procedures for control on the grid are computed and the Nash dynamic equilibrium is constructed. The behaviour of trajectories generated by the guaranteeing controls is investigated. Examples are given. date: 1995 date_type: published publisher: Elsevier id_number: 10.1016/0021-8928(95)00125-5 iiasapubid: XJ-95-012 iiasa_bibnotes: [in Russian] creators_browse_id: 1610 full_text_status: none publication: Applied Mathematics and Mechanics volume: 59 number: 6 pagerange: 921-933 refereed: TRUE issn: 0021-8928 coversheets_dirty: FALSE fp7_type: info:eu-repo/semantics/article citation: Tarasyev, A.M. (1995). The solution of evolutionary games using the theory of Hamilton-Jacobi equations. Applied Mathematics and Mechanics 59 (6) 921-933. 10.1016/0021-8928(95)00125-5 .