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Contents Preface Notation Chapter 1 Introduction 1 1.1 Hierarchical Conflicts 1 1.2 Classical Approaches to Conflict Analysis 3 1.3 Research Objectives 6 1.4 Outline 8 Chapter 2 Graph Model for Conflict Resolution 10 2.1 Formal Definition of Graph Model 10 2.2 Joint Movement and Joint Unilateral Improvement 11 2.3 Option Form and Option Prioritization 13 2.4 Matrix Representation of Graph Model 14 2.5 Solution Concepts 16 2.6 Decision Support System: GMCR II 18 Chapter 3 A Lead-in Example: Water Diversion Conflicts in China 19 3.1 Water Resources in China 19 3.2 The South-North Water Diversion Projects in China 20 3.3 Graph Model of Water Diversion Conflict in China 24 3.3.1 Decision Makers 24 3.3.2 Options 25 3.3.3 The Status Quo State 26 3.3.4 Removing Infeasible States 26 3.3.5 Ranking of Feasible States 27 3.4 Stability Analysis of the Hierarchical Water Diversion Conflict in China 29 3.4.1 Stability Calculation of the Hierarchical Conflict 293.4.2 Stability Analysis of the Separate Conflicts for the Three Routes 30 3.5 Comparison of the Three Separate Conflicts with the Overall Dispute 32 3.6 Summary 33 Chapter 4 Basic Hierarchical Graph Model with Lexicographic Preference 35 4.1 Formal Definitions 35 4.1.1 Framework of Basic Hierarchical Graph Model 36 4.1.2 Lexicographic Preference 38 4.2 Moves and Improvements 40 4.3 Interrelationships of Stabilities between Basic Hierarchical Graph Model and Local Graph Models 41 4.3.1 Nash Stability (R) 42 4.3.2 Sequential Stability (SEQ) 43 4.3.3 General Metarationality (GMR) 46 4.3.4 Symmetric Metarationality (SMR) 47 4.4 Water Diversion Conflicts in China 49 4.4.1 Conflict Modeling 50 4.4.2 Stability Analysis 53 4.4.3 Outcome Interpretation 56 4.4.4 Comparison of the Two Case Studies in Chapter 3 and Section 4.5 57 4.5 Summary 58 Chapter 5 Basic Hierarchical Graph Model in Matrix Form with Weighted Preference 59 5.1 Formal Definitions 59 5.1.1 Weighted Preference 60 5.1.2 Connection with Lexicographic Preference 61 5.1.3 Reachable Matrix 61 5.1.4 UI Matrix 62 5.1.5 Joint Movement and Improvement Matrices 63 5.2 Stability Definitions 63 5.3 Interrelationship Between Stabilities in the Hierarchical Graph and the Local Graphs 64 5.3.1 Nash Stability (R) 65 5.3.2 Sequential Stability (SEQ) 65 5.3.3 General Metarationality (GMR) 67 5.3.4 Sequential Metarationality (SMR) 68 5.4 Algorithms for Calculating Stability 69 5.4.1 Nash Stability (R) 69 5.4.2 Sequential Stability (SEQ) 69 5.4.3 General Metarationality (GMR) 71 5.4.4 Symmetric Metarationality (SMR) 71 5.5 Reinvestigation of Water Diversion Conflicts in China 72 5.6 Comparison of Weighted Hierarchical Graph Model and Former Methodologies 77 5.7 Summary 78 Chapter 6 Duo Hierarchical Graph Model 79 6.1 Formal Definitions 79 6.1.1 Definition of Duo Hierarchical Graph Model 79 6.1.2 Lexicographic Preference Structure 81 6.2 Sales Competition between Airbus and Boeing 82 6.2.1 Decision Makers and Their Options 83 6.2.2 States in the Sales Competition 85 6.2.3 Preferences of Decision Makers 86 6.2.4 The Uncertainty of Preferences for LDMs 87 6.2.5 Stability Calculation 90 6.2.6 Comparison with the Results in Separate Competitions 94 6.3 Summary 97 Chapter 7 General Hierarchical Graph Model 98 7.1 Formal Definitions 98 7.2 Preference Structures based on Option Prioritization 100 7.3 Interrelationships of Stabilities between General Hierarchical Graph Model and Local Graph Models 104 7.3.1 Nash Stability (R) 1047.3.2 Sequential Stability (SEQ) 104 7.3.3 General Metarationality (GMR) 105 7.3.4 Symmetric Metarationality (SMR) 106 7.4 Steps for Calculating Stabilities 106 7.5 Greenhouse Gas Emissions Disputes between China and USA 107 7.5.1 Conflict Background 107 7.5.2 Conflict Modeling 108 7.5.3 Removal of Infeasible States 112 7.5.4 Stability Analysis 112 7.5.5 Evolution of the Conflict 115 7.5.6 Implications for Decision Makers 116 7.5.7 Comparison of Stability Results 117 7.6 Summary 119 Chapter 8 Conclusions and Further Study 120 8.1 Major Contributions 121 8.2 Assumptions and Limitations of Hierarchical Graph Models 122 8.3 Further Study 123 References 125 Appendix A Proofs for Theorems 134 A.1 Proof for Theorem 4.1 134 A.2 Proof for Theorem 4.3 134 A.3 Proof for Theorem 4.4 135 A.4 Proof for Theorem 4.6 136 A.5 Proof for Theorem 4.7 137 A.6 Proof for Theorem 4.8 138 A.7 Proof for Theorem 4.11 139 A.8 Proof for Theorem 4.12 139 A.9 Proof for Theorem 5.1 141 A.10 Proof for Theorem 5.2 142 A.11 Proof for Theorem 5.4 144 A.12 Proof for Theorem 5.6 145 A.13 Proof for Theo