Both of the two major components of Game Theory, e.g., the non-cooperative game theory and the cooperative game theory, are becoming more and more closely related to the field of optimization, as the needs to study the analytical properties of games start to rise. The results presented in this thesis illustrate several connections between Optimization and Game Theory, and attempts are made to build a bridge between the cooperative game theory and the non-cooperative game theory, to characterize the co-existence of competition and cooperation in practice. We start by applying the properties of Polymatroid Optimization to the cooperative game theory, and show that both of the joint replenish game and the one warehouse multi retailer game are submodular games. In the next part, we show that the strategies promoting learning from history are convergent under certain conditions. This result can also be viewed as an efficient algorithm to compute the Nash Equilibrium of the game. Because the competitive routing game satisfies the condition, we know that if every user adapts with good enough memory, then asymptotically the system converges to Nash Equilibrium. Therefore, if the decision of cooperation is difficult to reverse, then it can be justified for the farsighted players to use the cost structure in the Nash Equilibrium point to decide if they should cooperate or not, instead of reacting to the immediate consequences as a basis to make decisions. With the optimization tools applied, we are able to show that in parallel network, the social cost and the cost of other players tend to decrease if two players cooperate. Also, the price of anarchy is higher when the flow demand of players are more evenly distributed. Using that structural result, we derive the exact upper bound of the price of anarchy for a given parallel network with fixed number of players. The exact upper bound of the price of anarchy for arbitrary parallel network with given number of players, which is independent to the network structure and parameters, can be derived consequently. / Simai He. / Adviser: Shuzhong Zhang. / Source: Dissertation Abstracts International, Volume: 72-11, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 97-103). / 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, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

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.