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Tools of Game Theory in Economic Decision Making
Šebedovský, Richard ; Studený, Václav (oponent) ; Mezník, Ivan (vedoucí práce)
This thesis deals with the present trends in application of game theory to creation of economic models, which are subsequently used in economic decision making with the support of tools of information technology. It mainly focuses on the tools of static and dynamic games and games with perfect and imperfect information. Models of resource sharing, auctions and management are under investigation. For each of the described models a concrete application is presented.
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Game Theory in Waste Management
Osička, Ondřej ; Vašík, Petr (oponent) ; Hrdina, Jaroslav (vedoucí práce)
In this thesis, a game-theoretic model representing a decision-making situation in the waste management is created as a noncooperative game representing the conflict of waste processors and a cooperative game representing the conflict of waste producers. For the conflict of waste processors, the Nash equilibria are used to find stable strategies on gate fee values, which serve as a good prediction for the future. To specify the strategy sets, a lower bound and an upper bound are determined. For the conflict of waste producers, assuming a cooperation among all of them, a cost distribution is determined using the Shapley value and the nucleolus. For more producers, approximation algorithms for the Shapley value and the nucleolus are developed. These algorithms are based on an assumption that distant producers can not influence each other. The model is applied to a situation in the Czech Republic. For the conflict of waste processors, one Nash equilibrium is found. For the conflict of waste producers, some producers with high potential in cooperation are recognized.
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Teorie her na grafech
Osička, Ondřej ; Vašík, Petr (oponent) ; Hrdina, Jaroslav (vedoucí práce)
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.
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Hraní stolní hry Stratego počítačem
Irovský, Dominik ; Šátek, Václav (oponent) ; Zbořil, František (vedoucí práce)
Tématem této práce je desková hra s neúplnou informací Stratego. Cílem je průzkum a zhodnocení dosavadních řešení hraní počítačem, návrh, implementace a testovaní vlastního řešení hraní počítačem. Pro vlastní řešení byl zvolen modifikovaný algoritmus Monte Carlo Tree Search. Řešení bylo realizováno jako konzolová aplikace s možností rozšíření. Funkcionalita implementace byla validována a otestována pomocí experimentů. Efektivita výsledného algoritmu byla uspokojivá.
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Počítačem řízený hráč hry Blokus založený na metodách umělé inteligence
Sulaiman, David ; Hrubý, Martin (oponent) ; Rogalewicz, Adam (vedoucí práce)
Tato práce se zabývá porovnáváním dopředných neuronových sítí s algoritmy teorie her pomocí deskové hry Blokus. V teoretickém úvodu jsou popsány vlastnosti neuronových sítí a~práce s nimi a zároveň jsou nastíněny algoritmy teorie her. Druhá část se věnuje implementaci jednotlivých hráčů založených na popsaných principech a stručnou charakteristikou grafického uživatelského rozhraní aplikace. V závěru práce byly provedeny testy hodnotící jednotlivé hráče, které byly zpracovány do grafů.
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Strategická hra s inteligentními prvky
Snášel, Lukáš ; Samek, Jan (oponent) ; Zbořil, František (vedoucí práce)
Cílem práce bylo navrhnout samofungující systém, který na základě teorie her a multiagentních systémů bude schopen dosáhnout svých cílů. Prezentací tohoto systému je strategická bojová tahová hra s grafikou vykreslenou pomocí DirectX9 a implementovaná v jazyce C++. Hlavním cílem bylo navrhnout vhodné prohledávací, plánovací a rozhodovací algoritmy.
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Topological Properties of Generalized Context Structures
Chernikava, Alena ; Chvalina, Jan (oponent) ; Beránek,, Jaroslav (oponent) ; Kovár, Martin (vedoucí práce)
This work is focused on the interaction of several branches of mathematics. The main idea was to nd dependencies, relationships and analogies between them. First part of the work is concerned to the relationship between Formal Concept Analysis, General Topology and Partial Metrics. A formal context is a very general mathematical structure that can represent other mathematical structures in a unied form. In a natural way, we could represent an information in a cross-table-like view of a formal context (fully respecting all set-theoretical limitations) and generate a topology on an attribute and object sets. In the second part the we study especially the pretopological systems as a special case of the formal contexts. They dier from topological systems especially by a more general poset structure of the set of attributes, representing the generalized open sets. Since the properties of this order structure are essential for the behavior of the whole structure, we pay them a special attention at the end of the chapter. Among others, we construct and study an analogue of the de Groot dual for posets, including its iteration properties. The third part is devoted to a mathematical structure called framework that has a contextual nature. A framework consists of two sets, rst one is a set of places, and the second one is a family of some its subsets, without the necessity of any external axioms to be fullled. The structure is equipped with a simple duality construction, allowing to switch between the classical point-set representation (like in topological spaces) and the point-less representation of topological relationships. At the end of the chapter, we suggest and study how a framework could be approximated by a directed family of nite frameworks from the point of view of the generated topology. In the last part the general topology methods were used to correct and improve one of the fundamental theorems in the game theory. It was showed that in a normal form game if i-th player has a continuous utility function and if the set of his strategies is almost-compact then he has an undominated strategy. In addition to this result, in the last two chapters we show that game theory naturally generates very general, for instance non-Hausdor topological and context structures, which shifts the traditional perception of reality in unexpected direction.
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Game Theory in Waste Management
Eryganov, Ivan ; Hoff, Arild (oponent) ; Kopa, Miloš (oponent) ; Hrdina, Jaroslav (vedoucí práce)
Game theory handles tasks such as cooperation, competition, and self-regulation in the environment, where numerous agents with conflicting goals are involved. These conflicts of interest are extremely common, when dealing with environmental sustainability and circular economy. This Ph.D. thesis is devoted to applications of game theory in waste management, with an emphasis on Waste-to-Energy treatment of non-recyclable waste. After an introduction, the fundamental background of game theory is summarized, providing an overview of the current state of knowledge. Then, recent applications of game-theoretic techniques in sustainability research are reviewed to emphasize the novelty of the work. In the end, the author's own contribution in the application of non-cooperative and cooperative games to problems of waste management is presented. In particular, this Ph.D. thesis is focused on the Waste-to-Energy plants' price-setting game and the waste producers' cost minimization game. Theoretical properties of these games are studied in detail. The original algorithms for bilevel optimization problems and dynamic coalition formation are proposed to solve the considered games. The case studies' results demonstrate rational outcomes of the conflicts and prove that the proposed approaches to the considered waste management problems are reasonable.
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Shapleův vektor v ekonomii
Maruniaková, Zuzana ; Návrat,, Aleš (oponent) ; Hrdina, Jaroslav (vedoucí práce)
Táto bakalárska práca sa zaoberá analýzou kooperatívnych hier, Shapleyho hodnotou a následnou aplikáciou na ekonomické a iné oblasti ľudského záujmu s využitím matematických metód. V práci sú špecifikovené dôležité pojmy a vlastnosti demonštrované na príkladoch. Ďalej sú popísané vybrané triedy koaličných hier a aplikácie Shapleyho hodnoty v praxi. Tieto poznatky sú využité v modele o voľbách.
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