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Two person quantum game theory
Krajný, Matěj ; Vašík, Petr (referee) ; Hrdina, Jaroslav (advisor)
This thesis presents introductuion to mathematical notation of quantum states, furthermore foucuses on deeper understanding of their representation. We broaden a clasical game of two players Prisoners dilema by adding quantum strategies. And we observe changes of equilibrium in comparison to clasical game.
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Prisoner's Dilemma
ČAPKOVÁ, Tereza
This thesis deals with studying the prisoner's dilemma in an iterated form, which represents a way of playing this game when players compete in multiple rounds and have the opportunity to change their strategy based on experience from previous games. The aim of the thesis is to evaluate suitable strategies for the iterated prisoner's dilemma based on information about the other player, such as gender, age, or other characteristics. The thesis also focuses on analyzing which player information is significant for changing player behavior and to what extent player strategies coincide with known strategies from AI tournaments. The introductory part of the thesis presents basic concepts of game theory and the prisoner's dilemma. Important terms related to the iterated form of the game, such as repeated play, the possibility of strategy change, and cooperation between players, are also explained. Classic prisoner's dilemma strategies, such as Dove, Hawk, and Copycat, are also introduced. In the practical part of the thesis, a web application is described that was created to simulate an economic conflict between a customer and a craftsman. This application allows players to play the iterated prisoner's dilemma and change their strategy based on experience from previous games. The application contains various AI strategies that players can play against. Player behavior data is collected and subsequently analyzed using observations and statistical methods. The results of this thesis show that there is almost no difference in play between men and women, and significant differences can only be observed between younger and older player groups. This assertion was verified in the thesis using a chi squared test. In conclusion, an optimal strategy was found against different player groups, which is cooperation throughout and betrayal in the final round.
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Two person quantum game theory
Krajný, Matěj ; Vašík, Petr (referee) ; Hrdina, Jaroslav (advisor)
This thesis presents introductuion to mathematical notation of quantum states, furthermore foucuses on deeper understanding of their representation. We broaden a clasical game of two players Prisoners dilema by adding quantum strategies. And we observe changes of equilibrium in comparison to clasical game.
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Game Theoretic Modelling of the International Relations System
Halás, Matúš ; Drulák, Petr (advisor) ; Plechanovová, Běla (referee) ; Křivan, Vlastimil (referee)
The thesis models interactions in the system of states. Fundamental research question asked what consequences for success of strategies and prospects of cooperative behavior have particular settings and properties of the system. Thesis includes two features peculiar to international relations that did not appear anywhere else before: (i) determination of interaction occurrence with help of distance and power; and (ii) emergence of (dis)trust out of the previous interactions. The model is based on three elements: agents, environment, and rules. Players interacted in the Hobbesian Prisoner's Dilemma environment as described by realists, but thanks to payoff shift representing emergence of (dis)trust I also formalized constructivist argument of different cultures of anarchy and of mutually constitutive agent-structure relationship. Multi-agent computer simulations set within the abductive reasoning framework were chosen because lack of heterogeneous enough data and impossibility of experiments made this data generating method a necessity. The source code is written in C#. I translated 62 Axelrod's behavioral rules and then added several others that seemed promising. Three new strategies mirroring usual behavior of states were proposed too. To secure robustness of the results, application was run...
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Quantum Theory of International Relations: Modeling Strategic Interaction with Quantum Probability Theory
Tesař, Jakub ; Drulák, Petr (advisor) ; Tyc, Tomáš (referee) ; Karlas, Jan (referee)
Recent results from cognitive psychology suggest that human behavior can be, in some situations, better described by laws known from physical quantum theory. This work responds to this development and seeks to answer the question of how quantum models of cognition and decision-making can contribute to our understanding of the social world. We introduce the approaches to the application of quantum theory in social sciences - quantum consciousness, quantum reasoning and quantum metaphor and further develop the second, in the context of strategic interaction in game theory. We show that the quantum model corresponds to both the psychological intuition and many empirically known anomalies such as the order effect, disjunction effect, or context effect. In this work, we derive a specific model of strategic interaction between two players, and we test it in the experimental Prisoner's Dilemma game. The model is based on the rational choice theory, which is nevertheless re-defined when it is shown how the strategic choice is changed if the quantum probability (C*-algebra) is used as the underlying theory instead of classical probability (σ-algebra). The results obtained support the quantum model and showed a different representation of the game among various groups of players. The quantum model of...
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Computational Problems Related to Graph Structures in Evolution
Šimsa, Štěpán ; Chatterjee, Krishnendu (advisor) ; Loebl, Martin (referee)
In this work we study certain stochastic game that illustrates the concept of punishment and that shows how punishment can improve cooperation. First we introduce the basics of game theory, Markov chains and stochastic games. Then we explain how evolutionary dynamics can be used to evaluate the expected amount of cooperation in a game. Finally we run simulations and do some numerical computations that show how punishment can improve cooperation. Powered by TCPDF (www.tcpdf.org)
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Replicator dynamics with mutations
Hrnčíř, Jakub ; Pražák, Dalibor (advisor) ; Kaplický, Petr (referee)
This thesis deals with the subject of implementing simplified principle of mutations into the replicator dynamics. In this thesis, I have shown the derivation of the basic replicator dynamics and on this basis I have derived generalized replicator dynamics with a deterministic model of mutations. Thesis also contains an analysis of general properties of these two models. Consequences of implementing mutations are demonstrated by means of analysis of three typical examples from the evolutionary game theory. I used the models called Hawk-Dove, Rock-Scissors-Paper and a modification of the Repeated Prisoner's Dilemma, to which I have paid the closest attention. The analysis shows in what ways the number of stationary points and their stability changes. Powered by TCPDF (www.tcpdf.org)
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Game Theoretic Modelling of the International Relations System
Halás, Matúš ; Drulák, Petr (advisor) ; Plechanovová, Běla (referee) ; Křivan, Vlastimil (referee)
The thesis models interactions in the system of states. Fundamental research question asked what consequences for success of strategies and prospects of cooperative behavior have particular settings and properties of the system. Thesis includes two features peculiar to international relations that did not appear anywhere else before: (i) determination of interaction occurrence with help of distance and power; and (ii) emergence of (dis)trust out of the previous interactions. The model is based on three elements: agents, environment, and rules. Players interacted in the Hobbesian Prisoner's Dilemma environment as described by realists, but thanks to payoff shift representing emergence of (dis)trust I also formalized constructivist argument of different cultures of anarchy and of mutually constitutive agent-structure relationship. Multi-agent computer simulations set within the abductive reasoning framework were chosen because lack of heterogeneous enough data and impossibility of experiments made this data generating method a necessity. The source code is written in C#. I translated 62 Axelrod's behavioral rules and then added several others that seemed promising. Three new strategies mirroring usual behavior of states were proposed too. To secure robustness of the results, application was run...
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Chování vybraných členských států EU v rámci dluhové krize (aplikace teorie her)
Novotný, Martin ; Dubský, Zbyněk (advisor) ; Sršeň, Radim (referee)
Thesis uses game theory to explain behavior of certain states in the European sovereign-debt crisis. The goal is to find out, if those states use strategies leading to equilibrium i.e. if they maximize their expected utility. Theoretical part is based mainly on repeated games and Bayesian game. Thesis summarizes development of European sovereign-debt crisis and key economic indicators. It constructs a game model of the crisis and further analyses situation of Germany, France, Italy, Spain and Greece as players in the game. The game model is then tested on key conflict situations such as relations of France and Germany, first Greek bailout negotiations or Spanish bank bailout negotiations. The results show that chosen states do maximize their expected utility in one election period. However maximization of utility in two or more election periods is limited by the parameters of democratic election system - length of election periods and information asymmetry between voters and politicians. The costs of elimination of information asymmetry would be higher than the costs of debt crisis. So even considering the costs of debt crisis the states are in long term equilibrium.
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