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Methods and Tools for Modelling of Multi-Comodity Markets
Janeček, Vítězslav ; Janoušek, Vladimír (referee) ; Hrubý, Martin (advisor)
This study investigates Game theory including economic theories related to agricultural production. Model creation simulating economical system is built upon theoretic starting points. Commodity production is simulated using game theory with searching for Nash equilibria. Commodity demand function is grounded on concept of Cournot game. System includes land trading based on sealed-bid auctions with second-price. This model is using external Gambit software which is freeware library for game theory computations. Model evaluation is located in Experiments section where model structure and truthfulness is tested.
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Game theory and poker
Schmid, Martin ; Hladík, Milan (advisor) ; Zimmermann, Karel (referee)
This thesis introduces the basic concepts of the game theory. Necessary models and solution concepts are described. Follows the summary of the computational complexity of these concepts and corresponding algorithms. Poker is formalized as one of the game theory game models. State of the art algorithms for the ex- tensive form games are explained with the application to the Poker. The thesis also introduces the Annual Computer Poker Competition and participating pro- grams. Finally, new result about the extensive form games with many actions is presented. Keywords: Game theory, Poker, Nash equilibrium, Extensive form games
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Artificial intelligence for Texas Holdem poker game
Moravčík, Matej ; Petříčková, Zuzana (advisor) ; Sýkora, Ondřej (referee)
Recently there has been a great expansion of poker. This includes live games, as well as games on the internet. For beginners, it may be difficult to find opponents skilled enough and thus improve their gaming performance without deposit of their own funds. Using of artificial intelligence seems as good solution for the problem, but there are only few suitable programs available. This thesis describes the overall design and development of such an application, specially designed for tournament variant of Texas Hold'em poker. Most attention is devoted to the artificial intelligence. There are two main approaches discussed - approximate Nash equilibrium and the use of expert system. Emphasis is placed on the first option. The main contribution of this thesis is detailed description and comparison of three algorithms for calculating the approximation of Nash equilibrium. Two of them are original heuristics algorithms, that take advantage of specific structure of poker game. Algorithms have been implemented and their properties have been empirically evaluated. The final result is a full-featured application designed for end users. It simulates poker game and provides a powerful artificial intelligence with attractive graphical user interface.
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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...
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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
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Solving Endgames in Large Imperfect-Information Games such as Poker
Ha, Karel ; Hladík, Milan (advisor) ; Bošanský, Branislav (referee)
Title: Solving Endgames in Large Imperfect-Information Games such as Poker Author: Bc. Karel Ha Department: Department of Applied Mathematics Supervisor: doc. Mgr. Milan Hladík, Ph.D., Department of Applied Mathematics Abstract: Endgames have a distinctive role for players. At the late stage of games, many aspects are finally clearly defined, deeming exhaustive analysis tractable. Specialised endgame handling is rewarding for games with perfect information (e.g., Chess databases pre-computed for entire classes of endings, or dividing Go board into separate independent subgames). An appealing idea would be to extend this approach to imperfect-information games such as the famous Poker: play the early parts of the game, and once the subgame becomes feasible, calculate an ending solution. However, the problem is much more complex for imperfect information. Subgames need to be generalized to account for information sets. Unfortunately, such a generalization cannot be solved straightaway, as it does not generally preserve optimality. As a consequence, we may end up with a far more exploitable strategy. There are currently three techniques to deal with this challenge: (a) disregard the problem entirely; (b) use a decomposition technique, which sadly retains only the same quality; (c) or formalize improvements of...
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Evaluating public state space abstractions in extensive form games with an application in poker
Moravčík, Matej ; Hladík, Milan (advisor) ; Zimmermann, Karel (referee)
Efficient algorithms exist for finding optimal strategies in extensive-form games. However human scale problems, such as poker, are typically so large that computation of these strategies remain infeasible with current technology. State space abstraction techniques allow us to derive a smaller abstract game, in which an optimal strategy can be computed and then used in the real game. This thesis introduces state of the art abstraction techniques. Most of these techniques do not deal with public information. We present a new automatic public state space abstraction technique. We examine the quality of this technique in the domain of poker. Our experimental results show that the new technique brings significant performance improvement. Powered by TCPDF (www.tcpdf.org)
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Game theory and poker
Schmid, Martin ; Hladík, Milan (advisor) ; Zimmermann, Karel (referee)
This thesis introduces the basic concepts of the game theory. Necessary models and solution concepts are described. Follows the summary of the computational complexity of these concepts and corresponding algorithms. Poker is formalized as one of the game theory game models. State of the art algorithms for the ex- tensive form games are explained with the application to the Poker. The thesis also introduces the Annual Computer Poker Competition and participating pro- grams. Finally, new result about the extensive form games with many actions is presented. Keywords: Game theory, Poker, Nash equilibrium, Extensive form games
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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...
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Artificial intelligence for Texas Holdem poker game
Moravčík, Matej ; Petříčková, Zuzana (advisor) ; Sýkora, Ondřej (referee)
Recently there has been a great expansion of poker. This includes live games, as well as games on the internet. For beginners, it may be difficult to find opponents skilled enough and thus improve their gaming performance without deposit of their own funds. Using of artificial intelligence seems as good solution for the problem, but there are only few suitable programs available. This thesis describes the overall design and development of such an application, specially designed for tournament variant of Texas Hold'em poker. Most attention is devoted to the artificial intelligence. There are two main approaches discussed - approximate Nash equilibrium and the use of expert system. Emphasis is placed on the first option. The main contribution of this thesis is detailed description and comparison of three algorithms for calculating the approximation of Nash equilibrium. Two of them are original heuristics algorithms, that take advantage of specific structure of poker game. Algorithms have been implemented and their properties have been empirically evaluated. The final result is a full-featured application designed for end users. It simulates poker game and provides a powerful artificial intelligence with attractive graphical user interface.
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