Conflict Resolution Using the Graph Model: Strategic Interactions in Competition and Cooperation (Studies in Systems, Decision and Control (153))

Preface
Acknowledgements
Contents
About the Authors
Acronyms
List of Figures
List of Tables
1 Conflict Resolution in Practice
	1.1 The Pervasiveness of Conflict
		1.1.1 Pressing Conflicts Facing Society
		1.1.2 Objectives of This Book
		1.1.3 Audience
	1.2 Investigating Conflict
		1.2.1 Key Ideas
		1.2.2 Modeling
		1.2.3 Stability Analysis
		1.2.4 Follow-Up Analyses
		1.2.5 Application Approaches
		1.2.6 Benefits
	1.3 Journeys Through the Book
	1.4 Problems
	References
2 Decision-Making in Perspective
	2.1 Overview
	2.2 Game Theory Methods: Classifications
		2.2.1 The Evolution of Game Theory Methods
		2.2.2 Classifying Formal Game Theory Techniques
	2.3 Formal Decision-Making Techniques
		2.3.1 Operations Research
		2.3.2 Systems Engineering
		2.3.3 Decision Support Systems
	2.4 Conflict Resolution in Responsible Governance
		2.4.1 System of Systems
		2.4.2 Integrative and Adaptive Management
	2.5 Important Ideas
	2.6 Problems
	References
3 Conflict Models in Graph Form
	3.1 Normal Form and Option Form
		3.1.1 Normal Form
		3.1.2 Option Form
	3.2 Graph Model
		3.2.1 Decision Makers
		3.2.2 States
		3.2.3 State Transitions
		3.2.4 Preferences
		3.2.5 Directed Graph
	3.3 Matrix Representation of a Graph Model
		3.3.1 Definitions from Algebraic Graph Theory
		3.3.2 A Rule of Priority to Label Colored Arcs
		3.3.3 Adjacency Matrix and Reachable List
		3.3.4 Preference Matrices
		3.3.5 Incidence Matrix and Graph Model
	3.4 Important Ideas
	3.5 Problems
	References
4 Stability Definitions: Simple Preference
	4.1 Simple Preference
		4.1.1 Reachable Lists of a Decision Maker
	4.2 Logical Representation of Stability Definitions
		4.2.1 Two Decision Maker Case
		4.2.2 Reachable Lists of a Coalition of Decision Makers
		4.2.3 n-Decision Maker Case
		4.2.4 Interrelationships Among Stability Definitions
	4.3 Matrix Representation of Stability Definitions
		4.3.1 Preference Matrices and UM and UI Matrices
		4.3.2 Two Decision Maker Case
		4.3.3 Matrices to Construct Reachable Lists of a Coalition
		4.3.4 n-Decision Maker Case
	4.4 Computational Complexity
		4.4.1 Two Decision Maker Case
		4.4.2 n-Decision Maker Case
	4.5 Application: Elmira Conflict
		4.5.1 Procedures for Calculating Stability
		4.5.2 Analysis of Stability Results
	4.6 Important Ideas
	4.7 Problems
	References
5 Stability Definitions: Unknown Preference
	5.1 Unknown Preference and Reachable Lists
		5.1.1 Reachable Lists of a Decision Maker
	5.2 Logical Representation of Stability Definitions Under Unknown Preference
		5.2.1 Two Decision Maker Case
		5.2.2 Reachable Lists of a Coalition
		5.2.3 Multiple Decision Maker Case
		5.2.4 Relationships Among Stabilities in the Graph Model with Preference Uncertainty
	5.3 Matrix Representation of Stability Definitions Under Unknown Preference
		5.3.1 Preference Matrices Including Uncertainty
		5.3.2 Two Decision Maker Case
		5.3.3 Reachability Matrices for a Coalition
		5.3.4 Multiple Decision Maker Case
		5.3.5 Computational Complexity
	5.4 Application: Lake Gisborne Conflict
		5.4.1 Procedures for Calculating Stability with Unknown Preference
		5.4.2 Reachability Matrices of a Coalition in the Gisborne Model
		5.4.3 Analysis of Stability Results for the Gisborne Model
	5.5 Important Ideas
	5.6 Problems
	References
6 Stability Definitions: Degrees  of Preference
	6.1 Multiple Degrees of Preference
		6.1.1 Three Types of Preference
		6.1.2 Multiple Degrees of Preference
	6.2 Reachable Lists of a Decision Maker
		6.2.1 Reachable Lists for Three Degrees of Preference
		6.2.2 Reachable Lists for Multiple Degrees of Preference
	6.3 Logical Representation of Stabilities for Three Types of Preference
		6.3.1 Two Decision Maker Case
		6.3.2 Reachable Lists of a Coalition of Decision Makers
		6.3.3 n-Decision Maker Case
	6.4 Logical Representation of Stabilities for Multiple Degrees of Preferences
		6.4.1 Two Decision Maker Case
		6.4.2 Reachable Lists of a Coalition of Decision Makers
		6.4.3 n-Decision Maker Case
		6.4.4 Interrelationship Among Stability Definitions for Multiple Degrees of Preference
	6.5 Matrix Representation of Stability Definitions for Three Degrees of Preference
		6.5.1 Preference Matrices Including Strength of Preference
		6.5.2 Two Decision Maker Case
		6.5.3 Reachability Matrix Under Strength of Preference
		6.5.4 n-Decision Maker Case
	6.6 Application: The Garrison Diversion Unit (GDU) Conflict
		6.6.1 Model of the GDU Conflict
		6.6.2 Stability Analysis Under Four-Degree Preference
	6.7 Important Ideas
	6.8 Problems
	References
7 Stability Definitions: Hybrid Preference
	7.1 Hybrid Preference and Reachable Lists
	7.2 Logical Representation of Stability Definitions Under Hybrid Preference
		7.2.1 Two Decision Maker Case
		7.2.2 Reachable List of a Coalition of Decision Makers Under Hybrid Preference
		7.2.3 n-Decision Maker Case
		7.2.4 Interrelationships Among Stabilities Under Hybrid Preference
	7.3 Some Important Matrices Under Hybrid Preference
		7.3.1 Preference Matrices Including Uncertainty and Strength
		7.3.2 Reachability Matrices Under Hybrid Preference
	7.4 Matrix Representation of Stabilities Under Hybrid Preference
		7.4.1 Matrix Representation of General Stabilities
		7.4.2 Matrix Representation of Strong and Weak Stabilities
	7.5 Application
	7.6 Important Ideas
	7.7 Problems
	References
8 Coalitional Stabilities
	8.1 Coalition Movement Definitions
	8.2 Logical Representation of Coalitional Stabilities Under Simple Preference
	8.3 Logical Representation of Coalitional Stabilities Under Unknown Preference
		8.3.1 Logical Representation of Coalitional Stabilities Indexed l
	8.4 Logical Representation of Coalitional Stabilities Under Three Degrees of Preference
		8.4.1 General Coalitional Stabilities
		8.4.2 Strong or Weak Coalitional Stabilities
	8.5 Logical Representation of Coalitional Stability with Hybrid Preference
		8.5.1 General Coalitional Stabilities with Hybrid Preference
		8.5.2 Strong Coalitional Stabilities with Hybrid Preference
	8.6 Matrix Representation of Coalitional Stability Under Simple Preference
		8.6.1 Coalitional Improvement Matrix
		8.6.2 Matrix Representation of Coalitional Stabilities
	8.7 Matrix Representation of Coalitional Stabilities Under Unknown Preference
		8.7.1 Matrix Representation of Coalitional Improvement or Uncertain Move
		8.7.2 Matrix Representation of Coalitional Stabilities Indexed l
	8.8 Matrix Representation of Coalitional Stability with Three Degrees of Preference
		8.8.1 Matrix Representation of Mild or Strong Coalitional Improvement
		8.8.2 Matrix Representation of General Coalitional Stabilities
		8.8.3 Matrix Representation of Strong Coalitional Stabilities
	8.9 Matrix Representation of Coalitional Stability  with Hybrid Preference
		8.9.1 Matrix Representation of Coalitional Improvement Under Hybrid Preference
		8.9.2 Matrix Representation of General Coalitional Stabilities with Hybrid Preference
		8.9.3 Matrix Representation of Strong Coalitional Stabilities with Hybrid Preference
	8.10 Application: Coalition Analysis for Lake Gisborne Conflict with Simple Preference
		8.10.1 Reachability Matrices in the Lake Gisborne Model
		8.10.2 Coalitional Stability Results in the Lake Gisborne Model
	8.11 Important Ideas
	8.12 Problems
	References
9 Follow-Up Analysis: Conflict Evolution
	9.1 Logical Representation of Conflict Evolution
		9.1.1 Simple Preference
		9.1.2 Unknown Preference
		9.1.3 Three Degrees of Preference
		9.1.4 Hybrid Preference
	9.2 Matrix Representation of Conflict Evolution  Based on Adjacency Matrix
		9.2.1 t-Legal Unilateral Move Matrix Under Various Preference Structures
		9.2.2 Status Quo Matrices Under Various Preference Structures
		9.2.3 Application: Status Quo Analysis for Elmira Conflict Under Simple Preference
	9.3 Matrix Representation of Conflict Evolution Based  on Edge Consecutive Matrix
		9.3.1 Weighted Conversion Function for Finding  Colored Paths
		9.3.2 Computer Implementation
		9.3.3 Procedures of Employing the Algebraic Approach Based on Edge Consecutive Matrix
		9.3.4 Applications: Analysis of Conflict Evolution Based on Edge Consecutive Matrix
	9.4 Important Ideas
	9.5 Problems
	References
10 Design of a Decision Support System for Conflict Resolution
	10.1 Decision Support Systems
		10.1.1 Introduction
		10.1.2 Existing Decision Support Systems for the Graph Model
	10.2 Universal Design of a Decision Support System  for the Graph Model
		10.2.1 Overall Design
		10.2.2 Input Subsystem
		10.2.3 Analysis Engine
		10.2.4 Output Subsystem
	10.3 Ongoing and Future Developments in the Graph Model Methodology
		10.3.1 Ongoing Expansions of the Graph Model
		10.3.2 Expansions of Systems Investigations in Conflict Resolution
	10.4 Problems
	References
Index