Kooperatīvās spēles un to analīze
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Latvijas Universitāte
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Abstract
Bakalaura darbs ir veltīts kooperatīvo spēļu analīzei. Darbā īpaša uzmanība tiek pievērsta spēļu normālformai. Tiek aprakstīts kā spēles ar nulles summu un spēles ar nenulles summu reducēt uz spēlēm normālformā un kā atrast to atrisinājumu izmantojot Šeplī vektoru. Darba sākumā ir ieskats matricu spēlēs. Ir dota spēles 0-1 reducētās formas analīze, tās atrisinājuma atrašana izmantojot C-kodolu un atrisinājumu pēc Neimana-Morgenšterna. Pielikums satur informāciju par ievērojamiem matemātiķiem, kuri devuši ieguldījumu spēļu teorijā.
Bachelor work is dedicated to analysis of cooperative games. Work is focused on normal form of games. Described how games with empty core as well as games with non-empty core reduce to games in normal form and how to solve them using Shapley’s vector. First part of work is about matrix games. Reduced game form 0-1 analysis is given, also it’s solution finding using C-core and von Neumann-Morgenstern solution. There is information about famous mathematicians, who gave their investment in game theory, collected in appendix.
Bachelor work is dedicated to analysis of cooperative games. Work is focused on normal form of games. Described how games with empty core as well as games with non-empty core reduce to games in normal form and how to solve them using Shapley’s vector. First part of work is about matrix games. Reduced game form 0-1 analysis is given, also it’s solution finding using C-core and von Neumann-Morgenstern solution. There is information about famous mathematicians, who gave their investment in game theory, collected in appendix.