Teorie her na grafech

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.