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Systems of Polynomial Equations in Economics
Šramková, Kristína ; Tomáš, Jiří (referee) ; Kureš, Miroslav (advisor)
Bachelor thesis is based on application of mathematical apparatus for the analysis of economic models, in particular models that lead to a system of polynomial equations. One of the parts is a summary of basic knowledge of algebra focused on Gröbner basis. Hereinafter are discussed economic models in which solution Gröbner basis are applied using the program Wolfram Mathematica. Own software package is implemented into this program as a concept of solution to simplify the calculation and work with models.
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Game Theory in Waste Management
Osička, Ondřej ; Vašík, Petr (referee) ; Hrdina, Jaroslav (advisor)
V této práci je vytvořen model rozhodovací situace v odpadovém hospodářství využívající metody teorie her. Model tvoří nekooperativní hra pro reprezentaci konfliktu zpracovatelů odpadu a kooperativní hra pro reprezentaci konfliktu producentů odpadu. Pro konflikt zpracovatelů odpadu je k nalezení strategií při volbě cen na bráně využit koncept Nashovy rovnováhy, takto nalezené stabilní strategie mohou sloužit jako předpověď budoucí situace. Pro zpřesnění množin strategií jsou určeny dolní a horní meze. Pro konflikt producentů odpadu se uvažuje spolupráce všech producentů a určuje se pro ni přerozdělení nákladů pomocí Shapleyho hodnoty a nucleolu. Pro konflikt více producentů jsou vyvinuty aproximační algoritmy pro Shapleyho hodnotu i nucleolus. Tyto algoritmy jsou založeny na předpokladu, že se vzdálení hráči vzájemně neovlivňují. Model je aplikován na situaci v České republice. Pro konflikt zpracovatelů odpadu je nalezen jeden bod Nashovy rovnováhy. Pro konflikt producentů odpadu jsou určeni někteří producenti s vysokým kooperativním potenciálem.
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Modelling of Dynamic Games with Imperfect Information
Straka, Richard ; Smrčka, Aleš (referee) ; Hrubý, Martin (advisor)
This work concentrates on the study of dynamic games; in particular games with imperfect information, implementation of a model and experimentation with the model. The game DarkElf was chosen for this project. It is a strategic, turn based game with economic and military features, where the decisions made by players are simultaneously implemented at a predetermined time.
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Tools of Game Theory in Economic Decision Making
Šebedovský, Richard ; Studený, Václav (referee) ; Mezník, Ivan (advisor)
Tato práce se zabývá současnými trendy v aplikaci teorie her k tvorbě ekonomických modelů, které se následně využívají při ekonomickém rozhodování s podporou prostředků informatiky. Práce se zejména opírá o poznatky teorie statických a dynamických her a her s dokonalými a nedokonalými informacemi. Zkoumány jsou modely týkající se sdílení zdrojů, aukcí a managementu. Pro každý z popsaných modelů je prezentována konkrétní aplikace.
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Spectrum auction and It's impact on telecommunication industry
Tománek, Petr ; Hořejší, Bronislava (advisor) ; Sirůček, Pavel (referee)
This work adresses oligopoly in telecomunication industry. Proper attention is given to the one of the biggest obstacles in entering the marker, which is acquiring the licence for the radio transmitting. Czech telecommunication Office decided to release these licences in a form of the auction. The work looks on the whole proces from the perspective of the game theory. Each participant is described and considered to be one of the players and regulatory agency as the rule maker of the game. Characteristics of the offered frequencies are alse discussed. The work investigates both of the carried out actions. Their results are examined and compared to the theoretical projections given by the game theory. Finally, a comparison with the auctions from the other european contries is given from the perspective of the outcome and defined rules.
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Decision situations in tournament poker
Preibisch, Jan ; Sekničková, Jana (advisor) ; Dlouhý, Martin (referee)
This thesis deals with factors which are important for making decisions in the game of poker. The goal is to find a way to improve players chances of success in this game. The first two chapters describe the rules of poker and the basics and presumptions of the game theory The following chapters analyze some mathematical models and assumptions for applying these models in the game. These models should find the optimal solution for individuals in decision making situations. It can be considered a static situation, where the behavior of each player is predetermined and the decision maker tries to find an appropriate strategy. It is also can be considered a dynamic situation, when all players react to each other, which heads to equilibrium solution. As a consequence of rising popularity of poker tournaments many strategy books have appeared, as well as analytic software. Nevertheless, it is and probably will remain impossible to solve all decision situations which can occur. A very important factor of success are some gamblers attitude, experience and mental skills. Mathematical knowledge, however, will become more and more important. This thesis will help to understand the basic of mathematic models and their application in poker game.
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Electricity market model of the Czech Republic
Kubát, Jan ; Pelikán, Jan (advisor) ; Kodera, Jan (referee) ; Marvan, Miroslav (referee)
A competitive electricity market has been established in many European countries including the Czech Republic. The electricity market includes a limited number of significant producers and traders, which can be described by oligopoly model. Since the electricity transmission and distribution are regulated, I consider two types of players performing in the electricity market: producers of electricity and traders, who buy electricity from producers and sell it to final customers. I derive oligopoly model with producers and traders "a la Cournot" and calculate a formula of equilibrium strategies. I use these theoretical findings to build a dynamic oligopoly model Ele. Ele is formulated as a mixed complementary problem and calibrated on data for the Czech Republic and neighbor states for several scenarios. The model was specified and calculated in GAMS software by the PATH solver. The results represent a Nash equilibrium. That means for individual producers: electricity generation, investment in new power plants construction and emission permits purchases. For traders the results are: equilibrium purchases, sales and cross-border transfers of electricity in each particular time period. Ele derives also equilibrium regional wholesale and retail electricity prices, emission permit prices and prices of cross-border auctions. Ele results point to an economic profitability of new nuclear power plants constructions. Further, I formulate a game in short-term electricity market, where I advise to Czech market participants, subjects of settlement, how much and in which circumstances to buy or sell electricity. Equilibrium results obtained through simulations based on the principle of a fictive game show that the current payment system of imbalance in the Czech Republic does not increase the risk of instability of electricity networks.
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Měnová politika a její synchronizace s fiskální politikou: vliv na hospodářský růst a inflaci
Řežábek, Pavel ; Schwarz, Jiří (advisor) ; Holman, Robert (referee) ; Komárek, Luboš (referee) ; Šimáček, Milan (referee)
The dissertation deals with the interplay of fiscal and monetary policy in face of uncertainty about the estimation of the true output gap. Theoretical framework of the dissertation set this interplay of monetary and fiscal policy into the realm of game theory, in particularly non-cooperative games of the Nash and Stackelberg equilibrium, respectively. The theoretical framework continued with a description of various methods used for estimation of potential output and output gap, with a special emphasis on methods used in both the Czech National Bank and Czech Ministry of Finance. In the applied part of the dissertation, I studied the interplay of monetary and fiscal policy in the case of Czech economy facing an uncertainty about the estimation of the true output gap. I studied the impact of this interplay on major macroeconomic variables and I tried to determine, which of these two policies plays the role of a leader and which plays the role of a follower in the case of Czech economic environment.
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Economy of Wealth and its Utilization in Practice
Budín, Pavel ; Musil, Martin (advisor) ; Havrdová, Romana (referee)
The goal is to describe the evolution of welfare economics from its beginnings to the present, to draw attention to the pitfalls of the various views and orientations, to evaluate the applicability of new welfare economics in terms of real economy and the example of the Republic or other countries (or EU) to indicate the possibilities of welfare economics or its part in practice, including positive and negative impacts on the economy and society. In the first part, which is part of the theoretical problems described welfare economics, and is also outlined the development of welfare economics. In the second part of the problem is applied to housing issues. Outlined here are the current problems associated with this phenomenon. The problem is under consideration from the perspective of welfare economics and its possible applications.
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