In the theory of open quantum systems, a quantum Markovian master equation, the Lindblad equation, reveals the most general form for the generators of a quantum dynamical semigroup. In this thesis, we present the derivation of the Lindblad equation and several examples of Lindblad equations with their analytic and numerical solutions. The graphs of the numerical solutions illuminate the dynamics and the stabilization as time increases. The corresponding von Neumann entropies are also presented as graphs. Moreover, to illustrate the difference between the dynamics of open and isolated systems, we prove two theorems about the conditions for stabilization of the solutions of the von Neumann equation which describes the dynamics of the density matrix of open quantum systems. It shows that the von Neumann equation is not satisfied for modelling dynamics in the cognitive contextin general. Instead, we use the Lindblad equation to model the mental dynamics of the players in the game of the 2-player prisoner’s dilemma to explain the irrational behaviors of the players. The stabilizing solution will lead the mental dynamics to an equilibrium state, which is regarded as the termination of the comparison process for a decision maker. The resulting pure strategy is selected probabilistically by performing a quantum measurement. We also discuss two important concepts, quantum decoherence and quantum Darwinism. Finally, we mention a classical Neural Network Master Equation introduced by Cowan and plan our further works on an analogous version for the quantum neural network by using the Lindblad equation.

Cooperating in the Prisoner's Dilemma is irrational and some supporting mechanism is needed to stabilize cooperation. Indirect reciprocity based on reputation is one such mechanism. Assessing an individual's reputation requires first-order information, i.e. knowledge about its previous behavior, as it is utilized under image scoring. But there seems to be an agreement that in order to successfully stabilize cooperation, higher-order information is necessary, i.e. knowledge of others' previous reputations. We show here that such a conclusion might have been premature. Tolerant scoring, a first-order assessment rule with built-in tolerance against single defections, can lead a society to stable cooperation. (author's abstract)

Part I focuses on studying the extent of cooperation in networked entities, within the context of the Prisoner's Dilemma (PD) and the Snowdrift Game (SG). The iterated prisoner's dilemma (IPD) is studied in the full payoff space spanned by two parameters beta and gamma. A theoretical study on two-strategy IPD is presented. We then numerically study the IPD in the full payoff space, with four different initial configurations. It is found that including the Tit-for-tat-like (ETFT) and Always-defecting-like (EAllD) strategies as initial strategies can maximize the dominating area of generous strategies in the payoff space at equilibrium. The roles played by ETFT and EAllD are further studied on the diagonal and anti-diagonal lines of the payoff space. / Part II focuses mainly on studying the optical properties of grating within the Rigorous Coupled-Wave Analysis (RCWA) method. The surface plasmon (SP) dispersion relation in a system consisting of a thin metallic film sandwiched between a linear dielectric and nonlinear dielectric of arbitrary non- linearity is derived, based on a generalized "first integral" approach. The SP dispersion relation in a system consisting of a thin metallic film sandwiched in a symmetric nonlinear dielectric environment is then derived. The changes in SP dispersion relations on film thicknesses are discussed for both cases. / The optical properties of two samples of one-dimensional metallic reflection gratings are studied. The numerical results of the zeroth order reflectance are in good agreement with experimental data. The Wood's anomaly occurs when a particular diffraction order emerges or disappears, thus inducing a change in the efficiency of other diffraction orders. This phenomenon is studied by calculating and measuring the efficiencies of all allowed diffraction orders. Numerical results of the near field patterns show a coupling between the waveguide and SP modes. We also study the controllable enhanced trans- mission in a semiconductor grating. The dielectric constant of a semiconductor becomes a tensor in the presence of a static magnetic field parallel to the slit. Numerical results based on RCWA reveal that the zeroth order transmission peaks at normal incidence can be shifted to longer wavelengths and the peak values of transmission can largely be enhanced when a moderate magnetic field is applied. A single-mode theory incorporating anisotropy is developed. The analytic results are in quantitative agreement with RCWA, indicating that the tunability in the transmission stems from the waveguide mode. / The Snowdrift Game is regarded as an important alternative to PD in studying the emergence of cooperation in competing populations. The phase transitions in spatial snowdrift games are introduced. By studying the relative alignments of the payoffs of C and D nodes, the phase transitions are analytically explained. As an extension to the standard two-person SG, an N-person Snowdrift Game (NPSG) is proposed to include generic multi-person interactions. NPSG in a well-mixed population is studied analytically by using the replicator dynamics. A simulation algorithm is developed. We also study NPSG on lattices and find a suppressed cooperation frequency, when compared with the well-mixed case. For NPSG played on 1D chain, the problem can be solved analytically. We further extend our work to study co-evolving dynamics. We propose and study a model in which the connections are driven to evolve by the dynamics of SG. Compared with played on static network, the cooperation frequency is promoted. A semi-analytic theory is proposed, with the results qualitatively agree with simulation results. / The thesis consists of two independent parts. Part I focuses on evolutionary games in networked entities and Part II focuses on calculations on optical properties of metallic gratings. / Yin, Haiping = 競爭群體中合作的產生及具規則結構之金屬薄膜的光學性質 / 尹海平. / Adviser: Hui Pak Ming. / Source: Dissertation Abstracts International, Volume: 72-04, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 185-200). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest Information and Learning Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese. / Yin, Haiping = Jing zheng qun ti zhong he zuo de chan sheng ji ju gui ze jie gou zhi jin shu bo mo de guang xue xing zhi / Yin Haiping.

Because the beer market in Taiwan had been opened up, the monopoly, Taiwan Beer, has been facing intense competition. However, state-owned Taiwan Beer uses flexible strategies to respond to these challenges and always is the leading company in the industry. This study tried to use Game Theory to analyze the competitive strategy of Taiwan Beer in different period of time and find out the relationships between Taiwan Beer and competitor. At the beginning, this research used Game theory to describe the competition in the beer industry. Then, it used Prisoner's Dilemma, the Beach Ice Cream Selling Model, entry-deny strategies, multi-brand strategy and Co-opetition to explain Taiwan Beer¡¦s interaction with others. Finally, this study did not see the competition as the only way that can help companies survive. When the company is thinking about how to defeat others, it also has to be thinking about how to cooperate with others to derive more advantages.

published_or_final_version / Psychology / Master / Master of Philosophy

Separate essays on entrepreneurship, joint venturing, and trade comprise this thesis. The emergence of entrepreneurship is common in the real world but relatively less so in classical economic models. If industry incumbents are attributed with full rationality and perfect foresight, then there are few, if any, profitable opportunities left for new entrants (entrepreneurs) to exploit. This essay explains how entrepreneurs can emerge in a dynamic world when firms must choose between a technology strategy that is either statically or dynamically efficient. A model is developed which shows how such opportunities for new entry can occur when incumbents are caught in a Prisoners’ Dilemma game involving technology strategy. A relevance measure and policy implications are then explored. Joint ventures, especially of the R&D type, are becoming increasingly important as a way to gain needed technological and market competencies. Unfortunately, many joint ventures have the characteristics of a Prisoners’ Dilemma. Firms may cooperate or defect in the venture. If contracts, side-payments, and third-party verification of the venture outcome are unavailable, then the dominant solution to the Prisoners’ Dilemma (mutual defection) results. This paper proposes the use of an ex-ante auction to obtain a Pareto-improvement for these ventures. A Pareto-improvement is assured when non-transferable costs and benefits of firms are not conditional on joint venture strategies. When this condition is not met restrictions are required to obtain the Pareto-improvement. The problem of trade between countries that share an international open access resource is becoming significant as the world reaches the limits of critical shared resource stocks. It is modelled as a world with one primary factor, two intermediate goods, one final good (harvested from the open access resource), and two nations where it is assumed that either the trading takes place over one stage (nations are price-takers), or two stages (nations have market power). Imperfect competition and open access generated externalities affect the trading efficiency. To maximize world welfare this essay recommends subsidizing R&D where comparative advantage exists, and creating international agreements to ensure the one-stage game structure is used when trading.

The Learning Classifier System (LCS) and its descendant, XCS, are promising paradigms for machine learning design and implementation. Whereas LCS allows classifier payoff predictions to guide system performance, XCS focuses on payoff-prediction accuracy instead, allowing it to evolve "optimal" classifier sets in particular applications requiring rational thought. This research examines LCS and XCS performance in artificial situations with broad social/commercial parallels, created using the non-Markov Iterated Prisoner's Dilemma (IPD) game-playing scenario, where the setting is sometimes asymmetric and where irrationality sometimes pays. This research systematically perturbs a "conventional" IPD-playing LCS-based agent until it results in a full-fledged XCS-based agent, contrasting the simulated behavior of each LCS variant in terms of a number of performance measures. The intent is to examine the XCS paradigm to understand how it better copes with a given situation (if it does) than the LCS perturbations studied.Experiment results indicate that the majority of the architectural differences do have a significant effect on the agents' performance with respect to the performance measures used in this research. The results of these competitions indicate that while each architectural difference significantly affected its agent's performance, no single architectural difference could be credited as causing XCS's demonstrated superiority in evolving optimal populations. Instead, the data suggests that XCS's ability to evolve optimal populations in the multiplexer and IPD problem domains result from the combined and synergistic effects of multiple architectural differences.In addition, it is demonstrated that XCS is able to reliably evolve the Optimal Population [O] against the TFT opponent. This result supports Kovacs' Optimality Hypothesis in the IPD environment and is significant because it is the first demonstrated occurrence of this ability in an environment other than the multiplexer and Woods problem domains.It is therefore apparent that while XCS performs better than its LCS-based counterparts, its demonstrated superiority may not be attributed to a single architectural characteristic. Instead, XCS's ability to evolve optimal classifier populations in the multiplexer problem domain and in the IPD problem domain studied in this research results from the combined and synergistic effects of multiple architectural differences.

Thesis (M.A.) - Carleton University, 2005. / Includes bibliographical references (p. 63-68). Also available in electronic format on the Internet.

Thesis (Ph. D.)--Ohio State University, 2008. / Title from first page of PDF file. Includes bibliographical references (p. 93-99).

Thesis (Ph.D.)--Psychology, Georgia Institute of Technology, 2009. / Committee Chair: Fredda Blanchard-Fields; Committee Member: Ann Bostrom; Committee Member: Christopher Hertzog; Committee Member: Jack Feldman; Committee Member: Paul Corballis