本論文包含四個部分。每一部分我們演示一個在共同演化網絡中的個體為本(agent-based)模型。第二章是不滿適應雪堆博奕(DASG)的廣泛化。第三章是自省適應(self-questioning adaptive)雪堆博奕。第四章是共同演化選民模型的廣泛化。第五章是有三個互相克制的角色的適應性石頭-布-剪刀(ARPS)模型。在這些模型中，適應行為導致共同演化過程發生。我們以電算模擬及理論方法研究這些模型。我們的目標是建立一個可應用於不同共同演化網絡的一般分析框架。 / 在第二章及第四章，我們將Gräser等人的DASG及Vazquez等人的共同演化選民模型從一個控制參數推廣到二個獨立的控制參數。在他們的工作中，根據網絡的結構定義了一些相，而且發展了平均場理論。而在廣泛化的情況下，在已伸延的相空間上，我們也定義了一些相及發展了一些廣泛化的平均場理論。在廣泛化DASG中，我們以考慮在相邊界附近的最終生存形態(last surviving patterns)以解釋相邊界的電算模擬結果。 / 在第三章，我們提出及研究一個以誘惑驅動的雪堆博奕。該更新機制被稱為自省機制(self-questioning mechanism)。我們給出模擬及理論結果，也討論了該些結果的物理意義。 / 在第五章，我們推廣我們的研究至有三個策略的遊戲。我們提出及研究了一個ARPS模型，其中每個個體採用三個互相克制的策略的其中之一。每個個體以概率 p來重連不理想的連結或以概率 (1 - p)改變自身的策略以適應其周遭環境。我們研究了網絡於不同的 p值在穩定態的行為及定義 了一些相。我們研究兩個選取重連對象的方法，分別對應於隨機選取及刻意選取重連對象，也解釋了得出的結果。我們在有關穩定勝利、平手及失敗概率的研究中及哪種個體可以有更高的勝利概率的研究中得出了有趣的結果。我們也研究了結果如何取決於初始條件。 / 在不同的模型中，理論方程均建立於相似的想法上。理論結果得出模擬結果的主要特性，包括出現了不同的相。該分析方法被證明了在本論文中對不同的模型也有效，而該方法也可被應用於很多其他共同演化網絡上。 / This thesis consists of four parts. In each part, we present results of an agent-based model of co-evolving network. Chapter 2 deals with a generalization of the Dissatisfied Adaptive Snowdrift Game (DASG) and Chapter 3 covers the self-questioning adaptive snowdrift game. Chapter 4 discusses a generalization of a co-evolving voter model. Chapter 5 gives the results on a cyclic three-character Adaptive Rock-Paper-Scissor (ARPS) game. The adaptive actions give rise to co-evolving processes in these models. These models are studied both numerically and analytically. An objective here is to establish a general analytic framework that is applicable to different models of co-evolving networks. / In Chapters 2 and 4, we generalize two existing models -the DASG of Gräser et al. and the co-evolving voter model of Vazquez et al. -from a single control parameter to two independent parameters. Different phases were identified according to the network structure and mean-field theories were developed in the previous work. With the expanded phase space in our generalized models, we identified different phases and provided a generalized mean-field approach. The phase boundaries in the generalized DASG can be explained by considering the last surviving patterns in the vicinity of the transition between two phases. / In Chapter 3, we propose and study a co-evolving snowdrift game in which the adaptive actions are driven by the desire to enhance winning. The updating scheme is called the self-questioning mechanism. We present simulation and theoretical results, and provide physical meaning to the results. / In Chapter 5, we extend our study to three-strategy games. An ARPS model in which each agent uses one of three strategies that dominate each other cyclically is proposed and studied. Each agent adapts his local environment by rewiring an un-favourable link with a probability p or switching his strategy with a probability 1-p. As p varies, the behaviour of the network in the steady state is studied and dierent phases are identified. Two dierent schemes corresponding to selecting the rewiring target randomly and intentionally are studied and the results are explained. Interesting results are also found in the probabilities of winning, losing and drawing in the steady state; and the type of agents that have a higher winning probability. The dependence on the initial distribution of the three strategies among the agents is also studied. / The analytic equations presented for each model in the thesis are established on similar ideas. The analytic results capture the main features in the simulation results, including the emergence of dierent phases. The analytic approach, proven to be useful through different models in this thesis, can be applied to a wide class of other co-evolving network models. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Choi, Chi Wun / 個體為本共同演化網絡的研究 / 蔡至桓. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 114-116). / Abstracts also in Chinese. / Choi, Chi Wun / Ge ti wei ben gong tong yan hua wang luo de yan jiu / Cai Zhihuan. / Abstract --- p.i / 摘要 --- p.iii / Acknowledgements --- p.v / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Introduction --- p.1 / Chapter 1.2 --- Review --- p.5 / Chapter 1.2.1 --- Network and basic graph properties --- p.5 / Chapter 1.2.2 --- Two-person games --- p.6 / Chapter 2 --- Generalization of Dissatisfied-Adaptive Snowdrift Game (DASG) --- p.8 / Chapter 2.1 --- Introduction --- p.8 / Chapter 2.2 --- Dissatisfied-Adaptive model --- p.12 / Chapter 2.3 --- Previous work --- p.14 / Chapter 2.4 --- Generalized Dissatisfied-Adaptive model --- p.16 / Chapter 2.5 --- Simulation results --- p.17 / Chapter 2.6 --- Theoretical analysis --- p.19 / Chapter 2.6.1 --- Mean-Field approach --- p.19 / Chapter 2.6.2 --- Theoretical results --- p.22 / Chapter 2.7 --- Last surviving patterns --- p.25 / Chapter 2.7.1 --- Observing the last surviving patterns --- p.25 / Chapter 2.7.2 --- Applying the theory using extracted information from simulations --- p.26 / Chapter 2.7.3 --- Further development of the theory --- p.28 / Chapter 2.7.4 --- Results of the theory --- p.30 / Chapter 2.8 --- Dependence on initial conditions and mean degree --- p.32 / Chapter 2.9 --- Conclusion --- p.34 / Chapter 3 --- Self-questioning Adaptive SG --- p.36 / Chapter 3.1 --- Introduction --- p.36 / Chapter 3.2 --- Self-questioning adaptive SG with control parameter r --- p.39 / Chapter 3.2.1 --- Model --- p.39 / Chapter 3.2.2 --- Results --- p.40 / Chapter 3.3 --- Self-questioning adaptive SG with control parameters r and h --- p.42 / Chapter 3.3.1 --- Model --- p.42 / Chapter 3.3.2 --- Results --- p.43 / Chapter 3.4 --- Conclusion --- p.45 / Chapter 4 --- Generalization of co-evolving voter model --- p.46 / Chapter 4.1 --- Introduction --- p.46 / Chapter 4.2 --- Co-evolving voter model --- p.49 / Chapter 4.3 --- Previous work --- p.50 / Chapter 4.4 --- Simulation results --- p.52 / Chapter 4.4.1 --- Results of macroscopic quantities --- p.52 / Chapter 4.4.2 --- Results of trajectories by simulations --- p.54 / Chapter 4.4.3 --- The largest component --- p.55 / Chapter 4.4.4 --- Short Summary --- p.56 / Chapter 4.5 --- Theoretical analysis --- p.57 / Chapter 4.5.1 --- Mean-Field approach --- p.57 / Chapter 4.5.2 --- Theoretical results --- p.59 / Chapter 4.6 --- Dependence on initial conditions and mean degree --- p.60 / Chapter 4.6.1 --- Results for different mean degrees --- p.60 / Chapter 4.6.2 --- Results for different initial conditions --- p.61 / Chapter 4.7 --- Conclusion --- p.63 / Chapter 5 --- Adaptive Rock-Paper-Scissors games --- p.64 / Chapter 5.1 --- Introduction --- p.64 / Chapter 5.2 --- Adaptive Rock-Paper-Scissors Model --- p.67 / Chapter 5.3 --- Simulation results --- p.70 / Chapter 5.4 --- Theoretical analysis --- p.73 / Chapter 5.4.1 --- Simplifications by threefold-symmetry --- p.73 / Chapter 5.4.2 --- Changes in local quantities --- p.74 / Chapter 5.4.3 --- Mean-Field approach --- p.75 / Chapter 5.4.4 --- Theoretical results --- p.80 / Chapter 5.5 --- Dependence on mean degree --- p.82 / Chapter 5.6 --- Oriented rewiring method --- p.83 / Chapter 5.7 --- Probabilities of winning, drawing and losing --- p.85 / Chapter 5.7.1 --- Average probabilities of winning, drawing and losing in the steady state --- p.85 / Chapter 5.7.2 --- Degree distribution and the distributions of the probabilities --- p.86 / Chapter 5.7.3 --- Brief explanation --- p.88 / Chapter 5.7.4 --- Results for a larger μ --- p.89 / Chapter 5.7.5 --- Short summary --- p.90 / Chapter 5.8 --- Results for general initial conditions --- p.92 / Chapter 5.8.1 --- Coupled dynamical equations --- p.92 / Chapter 5.8.2 --- Trajectories of the macroscopic quantities --- p.94 / Chapter 5.8.3 --- Phases and theoretical ternary phase diagrams --- p.96 / Chapter 5.9 --- Conclusion --- p.98 / Chapter 6 --- Summary --- p.100 / Chapter A --- Coupled dynamical equations for Self-questioning adaptive SG --- p.104 / Chapter B --- Theoretical results for Self-questioning adaptive SG with control parameters r and h --- p.106 / Chapter C --- Derivations of Mean-Field equations in ARPS model --- p.108 / Chapter D --- Derivations of Mean-Field equations for the oriented rewiring method in ARPS model --- p.111 / Bibliography --- p.114