Teorie her na grafech
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B
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Vysoké učení technické v Brně. Fakulta strojního inženýrství
Abstract
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.
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.
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Citation
OSIČKA, O. Teorie her na grafech [online]. Brno: Vysoké učení technické v Brně. Fakulta strojního inženýrství. 2014.
Document type
Document version
Date of access to the full text
Language of document
cs
Study field
Matematické inženýrství
Comittee
doc. RNDr. Miroslav Kureš, Ph.D. (předseda)
Ing. Josef Bednář, Ph.D. (místopředseda)
Mgr. Irena Hlavičková, Ph.D. (člen)
Mgr. Jana Hoderová, Ph.D. (člen)
doc. Mgr. Zdeněk Opluštil, Ph.D. (člen)
Date of acceptance
2014-06-19
Defence
Result of defence
práce byla úspěšně obhájena
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Standardní licenční smlouva - přístup k plnému textu bez omezení