Original title: Strategie a rovnováha v teorii her
Translated title: Strategies and equilibria in game theory
Authors: Mutňanský, Michal ; Milota, Jaroslav (advisor) ; Kaplický, Petr (referee)
Document type: Bachelor's theses
Year: 2012
Language: slo
Abstract: [eng] [cze]
Game theory is a discipline of applied mathematics that analyses a wide range of decision situations. In this thesis the reader is informed about the basic terms of game theory, some of them are illustrated on simple examples. The two dimensional Brouwer fixed-point theorem is proven using the Hex game. In addition to the formulation and proof of Nash's theorem, the thesis presents several methods for finding Nash equilibrium points, such as the simplex method. Their application to a specific game demonstrates the practical use of these methods. The thesis is intended for readers interested in the game theory, it does not, however, require any previous knowledge of this field of mathematics. Teória hier je disciplína aplikovanej matematiky, ktorá analyzuje široké spektrum konfliktných rozhodovacích situácií. V práci sa čitateľ zoznámi so základnými pojmami teórie hier, niektoré sú objasnené na jednoduchých príkladoch. Pomocou hry Hex je dokázaná Brouwerova veta o pevnom bode pre dimenziu 2. Okrem formulácie a dôkazu Nashovej vety o rovnovážnych bodoch práca približuje viacero metód hľadania týchto bodov, napríklad simplexovú metódu. Ich aplikáciou na jednu konkrétnu hru práca ukazuje praktické využitie týchto metód. Práca je určená pre čitateľov zaujímajúcich sa o teóriu hier, nepredpokladá však žiadne predošlé znalosti tejto oblasti matematiky.
Keywords: equilibrium; game; Nash's theorem; strategy; hra; Nashova veta; rovnováha; stratégia

Institution: Charles University Faculties (theses) (web)
Document availability information: Available in the Charles University Digital Repository.
Original record: http://hdl.handle.net/20.500.11956/42045

Permalink: http://www.nusl.cz/ntk/nusl-306345


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