|
|
A Tool for Analysis of Cooperative Games
Kessner, Filip ; Kočí, Radek (referee) ; Hrubý, Martin (advisor)
Cooperative games are most frequently used to simulate systems of the real world in which deal with cooperation and mutual agreement. Systems under investigation can be as simple as dispute over a shirt but investigated problems can be as crucial as designing of an electoral system, pollution cost allocation or protection of market competition as well. This thesis includes a graphical application capable of computation of some well-known solution types and selection of properties in cooperative games context.
|
|
|
Mayers Value in Economics
Karmazin, Alexandr ; Vašík,, Petr (referee) ; Hrdina, Jaroslav (advisor)
Bachelor thesis is focused on the coalition games in game theory. At the beginning, important terms that relate to these games are defined. Next part of the work is also the application of this knowledge to the real situation, namely the determination of the bargaining power of political parties in the Czech Republic using Myerson value. The work also includes custom application developed in mathematical software Matlab to calculate this value.
|
|
|
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.
|
|
|
Game theory on graphs
Osička, Ondřej ; Vašík, Petr (referee) ; Hrdina, Jaroslav (advisor)
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.
|
|
|
Cooperative game theory in dealing with local conflict
Ilavská, Adriana ; Mazal,, Jan (referee) ; Hrdina, Jaroslav (advisor)
The bachelor thesis is focused on introducing terms and solution concepts of the Cooperative Game Theory. The mathematical apparatus is then applied to the hypothetical local conflict in Scandinavia and in the countries of former Yugoslavia. The aim of the thesis is to point out the range of possibilities for using the Cooperative Games in the field of International Relations. For hypothetical conflicting situations, the potential gain of different coalitions is expressed by a characteristic feature. For the composed games is calculated the Shapley's value, expressing the fair distribution of profits between individual players, and Myerson's value, taking into account the impossibility of creating some of the coalitions. The work provides interpretations of results in the field of International Relations. It points out a wide range of possible applications of Cooperative Game Theory when conflicts occur at international scene, where this application is not common.
|
|
|
Shapley Value in Economics
Maruniaková, Zuzana ; Návrat,, Aleš (referee) ; Hrdina, Jaroslav (advisor)
The subject of this bachleor thesis is to introduce cooperative games, Shapley value and its application to economics and other human interests, using mathematical methods. This thesis is devoted to the important concepts and characteristics , which are illustrated by examples. The thesis also focused on describing selected classes of coalitional games and applications of Shapley´s value. These resulting findings are used in a model of election.
|
|
|
Cooperative interval games
Bok, Jan ; Hladík, Milan (advisor) ; Valla, Tomáš (referee)
In this thesis, we study cooperative interval games, a generalized model of cooperative games in which worth of every coalition corresponds with a closed interval representing all possible outcomes of their cooperation. We give a brief introduction into classical cooperative games, interval analysis and finally introduction to cooperative interval games with focus on selections, that is on all possible outcomes of interval game with no additional uncertainty. We introduce new selection-based classes of interval games and prove their characterizations and relation to existing classes. We show a new results regarding core and imputations. We introduce a definition of strong imputation and core and examine a problem of equality of two different versions of core -- the main stability solution of cooperative interval games. Finally, we make some new remarks on Shapley value of interval games.
|
|
|
Cooperative game theory in dealing with local conflict
Ilavská, Adriana ; Mazal,, Jan (referee) ; Hrdina, Jaroslav (advisor)
The bachelor thesis is focused on introducing terms and solution concepts of the Cooperative Game Theory. The mathematical apparatus is then applied to the hypothetical local conflict in Scandinavia and in the countries of former Yugoslavia. The aim of the thesis is to point out the range of possibilities for using the Cooperative Games in the field of International Relations. For hypothetical conflicting situations, the potential gain of different coalitions is expressed by a characteristic feature. For the composed games is calculated the Shapley's value, expressing the fair distribution of profits between individual players, and Myerson's value, taking into account the impossibility of creating some of the coalitions. The work provides interpretations of results in the field of International Relations. It points out a wide range of possible applications of Cooperative Game Theory when conflicts occur at international scene, where this application is not common.
|
|
|
Shapley Value in Economics
Maruniaková, Zuzana ; Návrat,, Aleš (referee) ; Hrdina, Jaroslav (advisor)
The subject of this bachleor thesis is to introduce cooperative games, Shapley value and its application to economics and other human interests, using mathematical methods. This thesis is devoted to the important concepts and characteristics , which are illustrated by examples. The thesis also focused on describing selected classes of coalitional games and applications of Shapley´s value. These resulting findings are used in a model of election.
|
|
|
Mayers Value in Economics
Karmazin, Alexandr ; Vašík,, Petr (referee) ; Hrdina, Jaroslav (advisor)
Bachelor thesis is focused on the coalition games in game theory. At the beginning, important terms that relate to these games are defined. Next part of the work is also the application of this knowledge to the real situation, namely the determination of the bargaining power of political parties in the Czech Republic using Myerson value. The work also includes custom application developed in mathematical software Matlab to calculate this value.
|
guest ::
