|
|
Weighted voting games and indexes of power
Schlosáriková, Eva ; Majer, Ondrej (advisor) ; Peliš, Michal (referee)
This thesis is an introducion to the theory of coalition games intended for readers oriented on formal disciplines (logic, mathematic, game theory) as well as on humanities (political science and sociology). Basic de nitions, characterization of voting systems, definition of weighted and unweighted voting systems are introduced. The next part of the thesis focuses on indexes of power (Shapley-Shubik, Banzhaf, Johnston, Deegan-Packel). The last part of thesis addresses the application indexes of power. Comparisons of indexes of the EU countries in decision-making proccesses of the Council of the European Union in accordance with the Treaty of Nice and the Treaty of Lisbon are presented.
|
|
|
Probabilistic semantics for Independence-friendly Logics
Seidl, Julian ; Majer, Ondrej (advisor) ; Švarný, Petr (referee)
(in English): Character of the work is purely theoretical and it pursues game theory in the perspective of mathematical logic and probability. The work is divided into two parts. Introductory part compiles basic concepts and definitions, summarizing the game theory and basics of syntax and semantics of mathematical logic and its extensions suitable for work in the field of game theory. Introductory part also explains following terms: extensive and strategic form of games, Nash equilibrium, pure and mixed strategies, winning strategies or independence-friendly logic. The problems solved in the second part of the work such as question of existence of Nash equilibrium in the games with infinite models or issue which arises when trying to uniformly distribute the probability of strategies in the same class of games are sketched out. The second part continues with analysis of strategic games with imperfect information aiming to the solution of nontrivial problems earlier proposed. Second part also introduces basic concepts and definitions of the probability theory, which helps comprehending the problems mentioned above. The last part of the work before the very presentation of some results induced by the area of infinite games is conversion between strategic and extensive games form. In the end of the...
|
|
|
An overview of selected social procedures
Schlosáriková, Eva ; Majer, Ondřej (advisor) ; Peliš, Michal (referee)
Title: An overview of selected social procedures Author: Eva Schlosáriková Department: Department of Political Science Supervisor: RNDr. Ondrej Majer, CSc. This thesis first defines social procedures. These are studied and analyzed by social soft- ware, an emerging interdisciplinary field. This thesis will focus on a prominent social procedure, the coalition bargaining and coalition formation. Basic definition and overview of the coalition theory are introduced. Last chapter will concentrate on Bram's model of the coalition formation and his definition of the stable coalition. Other models of the coalition bargaining are briefly introduced and compared to the Bram's model. Keywords: coalition bargaining, coalition formation, stability of coalition 1
|
|
|
Algorithmic complexity of solution concepts in selected classes of non-cooperative games
Wichera, Adam ; Majer, Ondřej (advisor) ; Kroupa, Tomáš (referee)
Title: Algorithmic complexity of solution concepts in selected classes of non-cooperative games Author: Adam Wichera Department: Department of Logic Supervisor: RNDr. Ondřej Majer, CSc. Supervisor's e-mail address: majer@ u.cas.cz Abstract In the presented work we study natural algorthmic problems rising from the concept of Nash Equilibrium. The problem of it's existence is trivial, because it follows from Nash The- orem of completeness of Nash Equilibria. Even related search problem doesn't seem to belong to NP-complete class, the reason being the very fact, that existence of Nash Equilibria is certain. Interesting observation is that every natural extension of this problem seems to be NP-complete. Many of such problems have been proven to be NP-complete through reduction of SAT problem, Klike problem or problem of searching subcover of certain size. The question, wheather the pro- blem of existence of assymmetric Nash equilibria of symmeric game ts with the others, in being NP-complete, has been an open problem. Here we show how to alternate the proof from [? ] and apply the construction to problem of existence of assymetric equilibria and therefore prove its NP-completness. Keywords: Nash equilibrium, Algorithmic complexity, Non-cooperative games, Game Theory, Assymetric equilibria, 1
|
|
|
Probabilistic semantics for Independence-friendly Logics
Seidl, Julian ; Majer, Ondrej (advisor) ; Švarný, Petr (referee)
(in English): Character of the work is purely theoretical and it pursues game theory in the perspective of mathematical logic and probability. The work is divided into two parts. Introductory part compiles basic concepts and definitions, summarizing the game theory and basics of syntax and semantics of mathematical logic and its extensions suitable for work in the field of game theory. Introductory part also explains following terms: extensive and strategic form of games, Nash equilibrium, pure and mixed strategies, winning strategies or independence-friendly logic. The problems solved in the second part of the work such as question of existence of Nash equilibrium in the games with infinite models or issue which arises when trying to uniformly distribute the probability of strategies in the same class of games are sketched out. The second part continues with analysis of strategic games with imperfect information aiming to the solution of nontrivial problems earlier proposed. Second part also introduces basic concepts and definitions of the probability theory, which helps comprehending the problems mentioned above. The last part of the work before the very presentation of some results induced by the area of infinite games is conversion between strategic and extensive games form. In the end of the...
|
|
|
Aplikace temporálních logik ve fyzice
Švarný, Petr ; Majer, Ondrej (advisor) ; Pudlák, Pavel (referee)
This thesis presents an introduction to the three main fields that study time: physics, philosophy, and logics. A brief introduction to general relativity, thermodynamics and quantum physics is made. Also some of the basic ideas from the philosophy of time are explained and dualities connected to time are described, e.g. eternalism vs. presentism, determinism vs. indeterminism and the reality or unreality of time. As there is a huge number of temporal logics, only the main ideas that differentiate these logics from others are pointed out and some typical proofs are then shown. Special attention is then given to the relation between logics and physics, how the first can be used in the latter. Thereafter, Branching space-times and Branching continuation models are presented, which proved to be useful within quantum physics. Next, some basic terminology connected to general relativity and the A, P and T topologies are introduced . These are used together with the given models to investigate a possible combination.
|
|
|
An overview of selected social procedures
Schlosáriková, Eva ; Majer, Ondřej (advisor) ; Peliš, Michal (referee)
Title: An overview of selected social procedures Author: Eva Schlosáriková Department: Department of Political Science Supervisor: RNDr. Ondrej Majer, CSc. This thesis first defines social procedures. These are studied and analyzed by social soft- ware, an emerging interdisciplinary field. This thesis will focus on a prominent social procedure, the coalition bargaining and coalition formation. Basic definition and overview of the coalition theory are introduced. Last chapter will concentrate on Bram's model of the coalition formation and his definition of the stable coalition. Other models of the coalition bargaining are briefly introduced and compared to the Bram's model. Keywords: coalition bargaining, coalition formation, stability of coalition 1
|
|
|
Weighted voting games and indexes of power
Schlosáriková, Eva ; Peliš, Michal (referee) ; Majer, Ondrej (advisor)
This thesis is an introducion to the theory of coalition games intended for readers oriented on formal disciplines (logic, mathematic, game theory) as well as on humanities (political science and sociology). Basic de nitions, characterization of voting systems, definition of weighted and unweighted voting systems are introduced. The next part of the thesis focuses on indexes of power (Shapley-Shubik, Banzhaf, Johnston, Deegan-Packel). The last part of thesis addresses the application indexes of power. Comparisons of indexes of the EU countries in decision-making proccesses of the Council of the European Union in accordance with the Treaty of Nice and the Treaty of Lisbon are presented.
|
|
|
Logical games and truth values
Majer, Ondrej
Formal game theory allows for an alternative view on logical systems: we can see verification of a certain statement as a game - formalized dialogue of two players. The rules of the game correspond to the properties of the system in the framework of which the statement is formalized. The article deals with the relation between properties of logical games and the number of truth values of the corresponding logical systems.
|
|
|
Games and the meaning of logical connectives
Majer, Ondrej
The main topic of the article is different understanding of logical connectives in logical systems (this is demonstrated on classical, intuitionistic and linear logic). The article focuses on the question how are the differences between the connectives captured in the game interpretation of the corresponding logical systems and on the adequacy of the game thoretical framework for characterising these differences.
|
guest ::
