博弈理論己貫穿於許多不同的研究領域中，成為了一種非常有用的研究工具。在演化博弈中，個體可以通過比較彼此在競爭中表現的好壞，從一個策略改變至另一個策略。當依賴於收益參數的競爭個體系統處於穩定態時，可以是一個所有個體都採用同一策略的均勻系統，或是使用不同策略的個體共同存在的非均勻系統。近年來，均勻態和混合態或是均勻相和混合相之間的轉變成為物理學家們的研究熱點。 / 在論文的第一部份(第二及第三章)中，我們研究了有空間關聯的群體在規則晶格上演化雪堆博弄(ESG) 。在文獻中的分析方法大多數是基於對近似法(pair approximation) 。但是對近似法的結果，就算是在定性上，都未能捕捉到電算模擬結果中顯現的重要特性。例如，對近似法未能給出全c 態和混合態之間以及混合態與全D 態之間的轉變特徵，其中c和D 分別表示演化雪堆博奔中的兩種策略。而這些轉變作為收益參數的函數，卻可於ESG 在不同的規則品格中的電算模擬中被觀察到。對近似法的這些缺陷引發了本論文的研究。當不同局域競爭組態的分佈形式假設為二項式分佈，並將之引入到c 個體數目隨時間演變的動態公式中，就能得出全D 態。當進一步深入考慮ESG 的演化後，我們得知在收益參數較小時，D 個體被孤立的局部組態的比例在二項式分佈假設中被高估。通過修正D 個體被孤立的局部組態比例，就能得出全C 態。通過適當調整收益參數較小時D 個體被孤立的局部組態的比例，和收益參數較大時適當調整C個體被孤立的局部組態的比例，我們就能得出與模擬結果吻合較好的結果。然後，我們還將這個方法推廣至線性鏈和六角品格結構中。該種方法比對近似法得到的結果更好。 / 在論文的第二部份(第四章)中，我們研究了有本懲罰者的存在對演化雪堆博弈在正方晶格上演化的影響。該博弈中相應地有三種策略。懲罰者願意支付額外成本以對不合作者造成顯外的損失。同時懲罰者與其他合作者之間是合作的。我們展示了在收益參數組成的空間下得出的詳盡相圖。我們從動態演化後期出現的最終生存形態(last surviving patterns) 出發，討論了相圖中的相邊界成因。 / Game theoretical methods have become a useful tool in research across many fields. In evolutionary games, agents could switch from one strategy to another based on how well they perform as compared with others. Depending on a payoff parameter, a system of competing agents may form a homogeneous system with all agents taking on the same strategy or an inhomogeneous system with the coexistence of different strategies in the steady state. The transitions between the homogeneous and mixed states or phases are of much interest to physicists in recent years. / In Part I (Chapter 2 and 3) of the thesis, the evolutionary snowdrift game (ESG) is studied in spatially structured populations on regular lattices. Analytic approaches in the literature are largely based on the pair approximation. However, results of the pair approximation cannot capture the key features in simulation results even qualitatively. For example, the pair approximation fails to give the transition between an All-C and the mixed phase and the transition between the mixed phase and an All-D phase as a function of a payoff parameter observed in ESG on different regular lattices, where C and D are the two strategies in ESG. The failure motivated the present work. By incorporating different local competing configurations within an assumption of binomial distribution into the dynamical equation for the time evolution of the number of C-agents, the All-D phase readily emerges. Further consideration of the dynamics of ESG informs us that the proportion of isolated-D local configurations is over-estimated in the binomial distribution when the payoffparameter is small. By modifying the proportion of isolated-D congurations, the All-C phase results. By suitably adjusting the weighings of isolated-D congurations for small payoff parameters and isolated-C congurations for large payoff parameters, good agreement with simulation results is obtained. The approach is then generalized to linear chain and hexagonal lattice. The present approach performs much better than the pair approximation. / In Part II (Chapter 4) of the thesis, the effects of the presence of costly punishers in ESG are studied in a square lattice. There are, thus, three strategies in the game. The punishers are willing to pay an extra cost so as to inflict an extra damage to a defector, and they cooperate with other cooperators. Detailed phase diagrams are presented in the space formed by the payoff parameters. The phase boundaries are discussed within the idea of last surviving patterns at the late stage of the dynamics. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Chan, Wan Hang = 晶格上演化雪堆博弈及相關問題的研究 / 陳運亨. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 81-86). / Abstracts also in Chinese. / Chan, Wan Hang = Jing ge shang yan hua xue dui bo yi ji xiang guan wen ti de yan jiu / Chen Yunheng. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Game Theory --- p.2 / Chapter 1.1.1 --- Prisoner Dilemma --- p.3 / Chapter 1.1.2 --- Snowdrift Game --- p.3 / Chapter 1.1.3 --- Costly Punishment --- p.4 / Chapter 1.2 --- Evolutionary Game Theory --- p.6 / Chapter 1.2.1 --- Updating Rules --- p.6 / Chapter 1.2.2 --- Updating Schemes --- p.6 / Chapter 1.2.3 --- Spatial Structures --- p.8 / Chapter 1.3 --- Analytic Approaches --- p.9 / Chapter 1.3.1 --- Mean-field Approach --- p.9 / Chapter 1.3.2 --- Last Surviving Patterns --- p.10 / Chapter 2 --- Evolutionary Snowdrift Game on Square Lattice --- p.11 / Chapter 2.1 --- Introduction --- p.11 / Chapter 2.2 --- Simulation Results --- p.12 / Chapter 2.3 --- Last Surviving Patterns --- p.15 / Chapter 2.4 --- Pair Approximation --- p.19 / Chapter 2.5 --- The Site Dynamical Equations --- p.22 / Chapter 2.5.1 --- Pure Binomial Approximation --- p.23 / Chapter 2.5.2 --- Modified Binomial Approximation --- p.24 / Chapter 2.5.3 --- Isolated Factor Correction --- p.27 / Chapter 2.5.4 --- The Zonal Correction --- p.31 / Chapter 2.6 --- Summary --- p.32 / Chapter 3 --- Evolutionary Snowdrift Game on Other Networks --- p.34 / Chapter 3.1 --- Snowdrift Game on Other Lattices --- p.34 / Chapter 3.1.1 --- Linear Chain --- p.34 / Chapter 3.1.2 --- Hexagonal Lattice --- p.40 / Chapter 3.2 --- Snowdrift Game on Small-world Network --- p.43 / Chapter 3.3 --- Summary --- p.50 / Chapter 4 --- Costly punishment in ESG on Lattices --- p.52 / Chapter 4.1 --- Introduction --- p.52 / Chapter 4.2 --- Model --- p.54 / Chapter 4.3 --- Simulation Results [1] --- p.56 / Chapter 4.3.1 --- Results with fixed α and β [1] --- p.56 / Chapter 4.3.2 --- Results with a fixed α [1] --- p.60 / Chapter 4.3.3 --- Consideration of special local structures --- p.65 / Chapter 4.3.4 --- Results of different α --- p.67 / Chapter 4.4 --- Pair Approximation Extended to Three Strategies [1] --- p.69 / Chapter 4.5 --- Summary --- p.76 / Chapter 5 --- Summary --- p.78 / Bibliography --- p.81 / Chapter A --- Uncertainty in Simulation Results --- p.87

The evolutionary processes of sexual selection are investigated in this study by developing a new model for the evolution of epigamic traits and examining the effects of male-male competition, female choice and filial cannibalism in a field population of the Cortez damselfish (Stegastes rectifraenum). Two general processes have been proposed to explain the evolution of epigamic traits: the good genes process and the Fisherian process. A third process leading to the evolution of epigamic traits is presented here: the good parent process. Epigamic traits arise through this process by clarifying the differences in non-heritable parental quality among potential mates. A population genetic model is developed, which further suggests that increases in the frequency of good fathers in the population and phenotypic plasticity enhance the evolution of a good parent trait. The relative strengths of female choice and male-male competition were studied in S. rectifraenum by direct observation of reproductive behavior, and through field experiments. Male body size was found to be the single most important correlate of male reproductive success. Males were removed from their territories to determine the extent to which the vacant territories were valued by other local males. All of the territories were quickly recolonized by new males and sites that initially showed the highest reproductive success continued to be the most successful when new residents were present. A second experiment involved standardizing nests in 30 territories. Under these conditions male body size was no longer correlated with reproductive success, indicating that females are strongly influenced by variance in natural nest sites. Consequently, male-male competition over territories containing high quality nest sites, in combination with female choice of those sites, generates the observed correlation between male body size and reproductive success. Partial clutch filial cannibalism by male S. rectifraenum was studied in the same population. A group of custodial males were fed eggs, while controls remained unfed. Both groups were dissected on the next day to determine the number of eggs in their stomachs. Fed males had significantly fewer eggs in their guts, indicating that they indeed feed on the eggs they guard, rather than take them incidently during nest maintenance activities. A second egg feeding experiment showed that male behaviour and reproductive success are little affected by filial cannibalism; thus it is hypothesized that the energy gained by this behaviour is channelled primarily into growth and survival.

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

Lee, Kwan Ho = 探討網絡上的若干動態過程 / 李鈞浩. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 114-118). / Abstracts in English and Chinese. / Lee, Kwan Ho = Tan tao wang luo shang de ruo gan dong tai guo cheng / Li Junhao. / Chapter 1 --- Overview --- p.1 / Chapter 2 --- Networks --- p.5 / Chapter 2.1 --- Describing Networks --- p.5 / Chapter 2.1.1 --- Adjacency Matrix --- p.6 / Chapter 2.1.2 --- "Degree, Degree Distribution and Mean Degree" --- p.6 / Chapter 2.1.3 --- Clustering Coefficient --- p.7 / Chapter 2.1.4 --- "Shortest Path, Shortest Distance and Diameter" --- p.7 / Chapter 2.1.5 --- Betweenness --- p.9 / Chapter 2.2 --- Barabasi-Albert (BA) Network --- p.10 / Chapter 2.2.1 --- Construction of BA Network --- p.10 / Chapter 2.2.2 --- Analytical Study of Degree Distribution --- p.11 / Chapter 2.2.3 --- Numerical Study of Degree Distribution --- p.12 / Chapter 2.2.4 --- Shortest Distance --- p.13 / Chapter 2.3 --- Summary --- p.14 / Chapter 3 --- Routing in Networks: A Review --- p.16 / Chapter 3.1 --- Introduction --- p.16 / Chapter 3.2 --- Dijkstra´ةs Algorithm --- p.17 / Chapter 3.2.1 --- Algorithm --- p.17 / Chapter 3.2.2 --- Running Time --- p.18 / Chapter 3.2.3 --- Routing Table Based on Shortest Path Algorithm --- p.19 / Chapter 3.3 --- Routing Model --- p.19 / Chapter 3.3.1 --- General Setup --- p.19 / Chapter 3.3.2 --- Phase Transition and Evaluation of Network Performance --- p.20 / Chapter 3.4 --- Using Shortest Path as Routing Algorithm on BA Networks --- p.21 / Chapter 3.5 --- Other Routing Algorithms --- p.22 / Chapter 3.5.1 --- Efficient Path --- p.23 / Chapter 3.5.2 --- Routing based on Local Structural Information --- p.24 / Chapter 3.5.3 --- Routing based on Dynamical Information --- p.25 / Chapter 3.6 --- Summary --- p.26 / Chapter 4 --- Optimization of Routing Efficiency through Redistributing Limited Resources --- p.28 / Chapter 4.1 --- A Reallocation Rule - Short to Long (S2L) --- p.29 / Chapter 4.2 --- Performance Enhancement After Applying S2L --- p.33 / Chapter 4.3 --- Optimized Capability Distribution in Detail --- p.36 / Chapter 4.4 --- Summary --- p.44 / Chapter 5 --- N-person Evolutionary Snowdrift Game: A Review --- p.47 / Chapter 5.1 --- Snowdrift Game (SG) and Evolutionary Snowdrift Game (ESG) --- p.47 / Chapter 5.2 --- N-person Evolutionary Snowdrift Game --- p.49 / Chapter 5.2.1 --- Payoffs of C-character and D-character Agents --- p.49 / Chapter 5.2.2 --- Replicator Dynamics --- p.50 / Chapter 5.2.3 --- Numerical Simulations --- p.52 / Chapter 5.3 --- Summary --- p.55 / Chapter 6 --- NESG on Complex Network --- p.56 / Chapter 6.1 --- Models --- p.57 / Chapter 6.2 --- Results of Model A (varying N) --- p.58 / Chapter 6.2.1 --- Correlation of Characters in Degree --- p.60 / Chapter 6.2.2 --- Correlation of Characters in Distance --- p.62 / Chapter 6.3 --- Results of Model B (Fixed-N) --- p.63 / Chapter 6.3.1 --- Correlation of Characters in Degree --- p.64 / Chapter 6.4 --- Summary --- p.69 / Chapter 7 --- Synchronization: A Review --- p.71 / Chapter 7.1 --- Kuramoto Model --- p.72 / Chapter 7.1.1 --- Analytical Method --- p.74 / Chapter 7.1.2 --- Numerical Method --- p.78 / Chapter 7.1.3 --- Summary of Kuramoto Model --- p.81 / Chapter 7.2 --- Integrate-and-Fire Model --- p.81 / Chapter 8 --- Kuramoto Model with Spatially Distributed Oscillators --- p.84 / Chapter 8.1 --- Model --- p.84 / Chapter 8.2 --- Numerical Results --- p.85 / Chapter 8.3 --- Analytic Results --- p.87 / Chapter 8.4 --- Summary --- p.90 / Chapter 9 --- Integrate-Fire-and-Run Model --- p.92 / Chapter 9.1 --- Model --- p.92 / Chapter 9.2 --- Two-Body System --- p.94 / Chapter 9.2.1 --- Case I: Oscillators A and B are in different sites --- p.94 / Chapter 9.2.2 --- Case II: Oscillators A and B are in the same site --- p.101 / Chapter 9.2.3 --- Comparison of Analytic Results and Numerical Simulations of Two-Body system --- p.103 / Chapter 9.3 --- N-Body System --- p.105 / Chapter 9.4 --- Summary --- p.111 / Chapter 10 --- Outlook --- p.112 / Bibliography --- p.114

Abstract not available

Despite the crucial importance of Hamilton's (1964) kin selection theory in evolutionary behavioral biology, psychological studies of family relationships have been relatively slow to incorporate a Darwinian perspective. One practical reason may be that existing evolutionary models of animal families, such as the honest signaling models, are applicable only if all family members fall into the same class in terms of age, sex, or health. The animal models are thus of limited use for investigating human families, in which the relative age of the child, as a corollary of birth order, may have played a pivotal role in shaping evolved family psychology. My dissertation has two main objectives: 1) to construct evolutionary mathematical models of family interactions that fully take into account the role of reproductive value and hence can be directly applied to human families; 2) to characterize the design features of evolved psychological mechanisms of human kinship by empirically testing a priori predictions derived from the models. I first examine how parents are expected to allocate their limited resources among offspring of differing ages. I show that the optimal strategy that serves parental interests is to bias parental resources toward the older offspring (chapter 2). I then empirically test the predictions derived from the first study, in comparison with previous evolutionary hypotheses of parental favoritism. The empirical results confirmed the predictions derived from the first study: in hypothetical allocation tasks, participants allocated more tangible resources toward older children (chapter 3). Next, I investigate how intrafamilial conflict over the allocation of parental resources occur when each family member (a parent, its senior offspring, and its junior offspring) are allowed to differ in age. The results gained in this study may require a substantial revision of Trivers' (1974) classical theory of parent-offspring conflict. Moreover, it will open a fruitful avenue for inferring the adaptive design of psychological mechanisms dealing with sibling relationships (chapter 4). I then show that evolutionary insights can be also applied to the psychological study of distant kin relationships such as cousins (chapter 5).