Original title: Teorie her na grafech
Translated title: Game theory on graphs
Authors: Osička, Ondřej ; Vašík, Petr (referee) ; Hrdina, Jaroslav (advisor)
Document type: Bachelor's theses
Year: 2014
Language: cze
Publisher: Vysoké učení technické v Brně. Fakulta strojního inženýrství
Abstract: [cze] [eng]
Tato prace se zabyva studiem teorie her a kooperativni teorie her v kombinaci s teorii grafu. Vyuzivanym matematickym modelem hry je zde hra ve tvaru s charakteristickou funkci. Pro urceni optimalniho rozdeleni zisku u kooperativnich her je zavedeno jadro hry a Shapleyho hodnota. Na prikladech je ukazan vyznam jejich pouziti. Z teorie grafu jsou zde vyuzity orientovane i neorientovane ohodnocene ci neohodnocene grafy pro reprezentaci vztahu mezi hraci a siti, na kterych se hra a mozna rozhodnuti hracu odehravaji. The subject of this thesis is to introduce game theory and cooperative game theory in relation to graph theory. Game in characteristic function form is used to model the cooperative game. The optimal division of payoff among the players is determined by means of Shapley value and game kernel. Examples of practical use are presented. To examine more complicated game network or to express relationship between players both directed and undirected graphs are used.
Keywords: cooperative game; game theory; graph theory; Shapley value; kooperativni hra; Shapleyho hodnota; teorie grafů; teorie her

Institution: Brno University of Technology (web)
Document availability information: Fulltext is available in the Brno University of Technology Digital Library.
Original record: http://hdl.handle.net/11012/31976

Permalink: http://www.nusl.cz/ntk/nusl-214463


The record appears in these collections:
Universities and colleges > Public universities > Brno University of Technology
Academic theses (ETDs) > Bachelor's theses