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Game of Markets
Dóczy, Aneta ; Novotná, Veronika (referee) ; Chvátalová, Zuzana (advisor)
This diploma thesis deals with conict economic situations based on game theory. In the beginning, basic models of conict situations and current popular software tools are dened not only for the general support of student education or for science, but also for solving economic problems in game theory. Based on this analysis, the conicting situation of two competing rms is being solved. Gradually, work goes deeper into areas of delay dierential equations that better show the behavior of two players on the market. Subsequently, these delayed dierential equations are projected into the Cournot model, for which a critical value is identied that switches the stability of two rms on the market due to the delayed realization of their outputs.
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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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Multiplatform Card Game with Artificial Intelligence
Trejtnar, Martin ; Chlubna, Tomáš (referee) ; Matýšek, Michal (advisor)
This thesis focuses on artificial intelligence in card games. The goal is to implement a multi-platform game of this genre in the Unity game engine, to summarize possible approaches that are being used in order to create intelligent agents and furthermore to design and describe the most suitable method or combination of methods for the chosen game. The research that was carried out has shown that the problem domain of card games is rather specific, making it more difficult to use the general-purpose algorithms. The problem given was solved using the rule-based artificial intelligence. The intelligent agent has been implemented for a game of imperfect information, which is considered to be the main contribution of this work to the community. Even though the artificial intelligence player is making minor tactical mistakes, his behavior closely resembles the way of thinking of semi-experienced players.
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Limit behavior of the Nash equlibrium
Kovařík, Vojtěch ; Spurný, Jiří (advisor) ; Bárta, Tomáš (referee)
The subject of study of game theory - games - serves as mathematical models for real-life problems. In every game there are two or more players who aim to maximize their own profit by choosing their actions. A situation where no player can benefit from changing his own action alone has got particular importance in the study of games - it is called Nash equilibrium. Games with a finite number of players have certain advantages over those with an infinite number of players. For one, problems whose model is a game with a finite number of players are quite common. Moreover, one of the classical results of game theory is that (with certain additional assumptions) in every game with a finite number of players there exists a Nash equilibrium. On the other hand, when trying to describe the properties of a game with an infinite number of players we might be able to use calculus instead of going trough all possibilities (as is common for games with a finite number of players), which tends to be computationally demanding. However, if we want to use these advantages of games with an infinite number of players, it is important first to know whether there is any relationship between games with a finite and infinite number of players at all. The goal of this thesis is to define terms and to introduce tools which would allow...
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Multiplatform Card Game with Artificial Intelligence
Trejtnar, Martin ; Chlubna, Tomáš (referee) ; Matýšek, Michal (advisor)
This thesis focuses on artificial intelligence in card games. The goal is to implement a multi-platform game of this genre in the Unity game engine, to summarize possible approaches that are being used in order to create intelligent agents and furthermore to design and describe the most suitable method or combination of methods for the chosen game. The research that was carried out has shown that the problem domain of card games is rather specific, making it more difficult to use the general-purpose algorithms. The problem given was solved using the rule-based artificial intelligence. The intelligent agent has been implemented for a game of imperfect information, which is considered to be the main contribution of this work to the community. Even though the artificial intelligence player is making minor tactical mistakes, his behavior closely resembles the way of thinking of semi-experienced players.
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Spatial agent-based models of common pool resources
Vach, Dominik ; Gregor, Martin (advisor) ; Červinka, Michal (referee)
This thesis examines the application of the spatial aspect applied in the com- petitive models in the context of the natural resource economics. At first, the spatial models are thoroughly derived in one dimension. Then also their general properties such as the choice of the agents' location or their payoff function are examined. These properties are investigated for various distri- butions of the resource, and therefore they depend also on their parameters. The Nash equilibrium and local stability conditions are derived for the basic setups. In the second part, these competitive models are numerically tested also in a two-dimensional space. One of the results also suggests, that in the setup where the players have perfect information, the beginning player is not necessarily always better off than the second player. Throughout the entire thesis it is also comprehensively examined whether the existence of corners of the strategy space has an impact on the existence of the competition which was successfully demonstrated on several cases. JEL Classification Q20, Q22, C62, C68, C72 Keywords spatial models, natural resource exploitation, Nash equilibrium, fishery, computer simulations Author's e-mail vach.dominik@gmail.com Supervisor's e-mail martin.gregor@fsv.cuni.cz 1
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(Non)rationality of betting
Hamáček, Filip ; Hlaváček, Jiří (advisor) ; Cahlík, Tomáš (referee)
The subject of this bachelors thesis is nonrationality of betting. The first part of thesis is discussing different instruments of risk evaluation. The second part is about Petersburg paradox. This thesis tries to find alternative solution to Petersburg paradox using two methods, the first method is based on repeating high amount of petersburg games. The second method is maximizing the probability of economic survival, which is based on wealth of the player and on bound of economic survival. In the third part of this thesis, Sportka (Czech lottery) is compared with special tournament of poker. The goal of this part is to compare the expected return of investment on playing Sportka and on playing poker without even basic notion about rules and the game strategy. For the estimation of the expected value of poker tournament, different game scenarios are considered, probability of scenarios are based on players behavior according to the Nash equilibrium. Keywords: Betting, expected value, Petersburg paradox, lottery, poker, Nash equilibrium
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Game of Markets
Dóczy, Aneta ; Novotná, Veronika (referee) ; Chvátalová, Zuzana (advisor)
This diploma thesis deals with conict economic situations based on game theory. In the beginning, basic models of conict situations and current popular software tools are dened not only for the general support of student education or for science, but also for solving economic problems in game theory. Based on this analysis, the conicting situation of two competing rms is being solved. Gradually, work goes deeper into areas of delay dierential equations that better show the behavior of two players on the market. Subsequently, these delayed dierential equations are projected into the Cournot model, for which a critical value is identied that switches the stability of two rms on the market due to the delayed realization of their outputs.
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Limit behavior of the Nash equlibrium
Kovařík, Vojtěch ; Spurný, Jiří (advisor) ; Bárta, Tomáš (referee)
The subject of study of game theory - games - serves as mathematical models for real-life problems. In every game there are two or more players who aim to maximize their own profit by choosing their actions. A situation where no player can benefit from changing his own action alone has got particular importance in the study of games - it is called Nash equilibrium. Games with a finite number of players have certain advantages over those with an infinite number of players. For one, problems whose model is a game with a finite number of players are quite common. Moreover, one of the classical results of game theory is that (with certain additional assumptions) in every game with a finite number of players there exists a Nash equilibrium. On the other hand, when trying to describe the properties of a game with an infinite number of players we might be able to use calculus instead of going trough all possibilities (as is common for games with a finite number of players), which tends to be computationally demanding. However, if we want to use these advantages of games with an infinite number of players, it is important first to know whether there is any relationship between games with a finite and infinite number of players at all. The goal of this thesis is to define terms and to introduce tools which would allow...
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