Contents
Preface
Chapter1 Introduction 1
1.1 Motivations 1
1.2 Outline of the Book 2
Chapter2 Influence Diagrams 3
2.1 Introduction 3
2.2 Preliminary 3
2.3 Influence Diagrams 9
2.3.1 Th e graphical component of an ID 9
2.3.2 The numerical component of an ID 11
2.4 Conclusion 14
Chapter3 The Extensions of Influence Diagrams 15
3.1 Introduction 15
3.2 Unconstrained Influence Diagrams (UIDs) 17
3.3 Limited Memory Influence Diagrams (LIMIDs) 19
3.4 Mixtures of Truncated Exponentials Influence Diagrams (MTE IDs) 20
3.5 Possibilistic Influence Diagrams (PIDs) 22
3.6 Interval-Valued Influence Diagrams (IIDs) 25
3.6.1 Bound-limited weak conditional interval probability 29
3.6.2 Influence diagrams with interval-valued parameters (BIIDs) 32
3.7 Game Theory-Based Influence Diagrams (GIDs) 33
3.7.1 Game theory 34
3.7.2 Game theory-based influence diagrams (GIDs) 36
3.8 Game IDs with Interval-Valued Parameters (GBIIDs) 39
3.9 Conclusion 41
Chapter4 The Evaluation of Influence Diagrams 42
4.1 Introduction 42
4.2 The Concept of Evaluating IDs 43
4.3 Evaluating Standard IDs 46
4.3.1 Arc reversal (AR) 46
4.3.2 Variable elimination(VE) 51
4.3.3 Cooper's method (CM) 54
4.4 Evaluating Interval-Valued IDs 57
4.4.1 Operations for interval-valued potentials 57
4.4.2 Interval arc reversal (IAR) 57
4.4.3 Interval variable elimination (IVE) 62
4.4.4 Chance variable and arc reversal elimination in IIDs by linear programming 65
4.4.5 Interval Cooper's method (ICM) for evaluating BIIDs 69
4.5 Evaluating GIDs 79
4.5.1 Concepts 79
4.5.2 The design of the genetic algorithm 82
4.5.3 The algorithm for evaluating GIDs (EAGIDs) 84
4.6 Evaluating Game IDs with Interval-Valued Parameters (GBIIDs) 89
4.6.1 Solving games with interval-valued utilities 89
4.6.2 Computing strategy utilities for utility nodes shared by multiple decision makers 90
4.6.3 Selecting the strategy with maximal interval-valued expect utility 92
4.7 Conclusion 93
Chapter5 Applications of Influence Diagrams 95
5.1 Finding Optimal Strategies for a Decision Maker by a BIID 95
5.2 Applying Influence Diagrams to Infer Rival's Private Information 99
5.2.1 The type of rival's private information 100
5.2.2 Inferring rival's private information 102
5.2.3 Experiments 104
5.3 Conclusion 107
References 109