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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.
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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.
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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.
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The development of micro-motor skills in cooperative activities
BARTÍKOVÁ, Irena
The bachelor thesis provides an inspirational material for pedagogical staff on the use of cooperative activities. One of the chapters from the theoretical part is focused on the issue of fine motor skills, their development, possibilities of growth and diagnostics. Another part defines cooperation and developmental traits considering the development of cooperation of preschool children. Last section of the theoretical part deals with cooperation as one of the goals of preschool education, development of cooperation, positive impacts of developing cooperation by games, basic components of cooperative game, cooperative learning and its rating. Practical part consists of development program for fine motor skills in cooperative activities and its evaluation, due to achieving goals in the field of fine motor skills, and cooperation by the pre-treated evaluation plan. In the conclusion of the thesis are summarized recommendations for application of these activities in nursery schools.
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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.
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Agent-based models of cooperative games
Sedláček, Adam ; Burian, Jan (advisor) ; Dlouhý, Martin (referee)
The diploma thesis describes design and creation of agent-based model of cooperative games and its subsequent analysis. The created model combines assumptions of game the-ory with other findings; it examines the dynamics of coalition formation and the influence of external and internal factors on this formation. The first theoretical part introduces the game theory and clarifies basic principles and con-cepts of N - player cooperative games. It evaluates the benefits and disadvantages of solu-tions introduced by this theory. The thesis further deals with multi-agent systems focused on agent-based models as an analytical and computational method for analyzing complex systems. There are also explained basic principles of agent-based modeling, including ap-proaches of their creation. Furthermore, there are presented distinctions between different types of agents, environments and models. The second practical part specifies assumptions and principles that are essential for the created multi-agent model. The diploma thesis describes the development of agent-based model of cooperative games by itself, including its characteristics and behavior. Final analysis of the created model clarifies impact of individual variables on the coalition for-mation process and confirms its ability to investigate given area.
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Fuzzy coalitional structures
Mareš, Milan ; Vlach, M.
The procedure of fuzzification of the coalitional game is described and analyzed. The main attention is paid to the specific properties of superadditivity and convexity in the fuzzified model.
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