Handbook of the Shapley Value 1st Edition by Encarnacion Algaba, Vito Fragnelli, Joaquin Sanchez Soriano ISBN 1351241419 9781351241410

Handbook of the Shapley Value 1st Edition by Encarnacion Algaba, Vito Fragnelli, Joaquin Sanchez Soriano – Ebook PDF Instant Download/Delivery: 1351241419, 9781351241410
Full download Handbook of the Shapley Value 1st Edition after payment

Product details:

ISBN 10: 1351241419
ISBN 13: 9781351241410
Author: Encarnacion Algaba, Vito Fragnelli, Joaquin Sanchez Soriano

Handbook of the Shapley Value 1st Table of contents:

1. The Shapley Value, a Crown Jewel of Cooperative Game Theory
1.1 Introduction
1.2 Coalitional Games and their Values
1.3 A Short Guide to the Chapters
1.4 Acknowledgments
Bibliography
2. The Shapley Value, a Paradigm of Fairness
2.1 Introduction
2.2 The Mathematical Expression
2.3 Some Characterizations
2.4 Some Extensions and Applications
2.5 Conclusions
2.6 Acknowledgments
Bibliography
3. An Index of Unfairness
3.1 Introduction
3.1.1 Organization and Data Set
3.1.2 The Shapley Value as an Ideal for Fairness
3.2 The Shapley Distance as a Measure of Unfairness
3.2.1 An Axiomatic Characterization of the Shapley Distance
3.2.2 A Decomposition of the Shapley Distance with Limited Data Sets
3.3 Some Applications
3.3.1 Favoritism
3.3.2 Egalitarianism versus Fairness
3.3.3 Taxes
3.4 Conclusions
3.5 Acknowledgments
Bibliography
4. The Shapley Value and Games with Hierarchies
4.1 Introduction
4.2 Games with Hierarchies
4.2.1 TU-Games
4.2.2 Digraphs
4.2.3 Games with a Permission Structure
4.2.4 Games under Precedence Constraints
4.3 Solutions for Games with Hierarchies
4.3.1 The Conjunctive Permission Value for Games with a Permission Structure
4.3.2 The Precedence Shapley Value and the Hierarchical Solution for Games under Precedence Constraints
4.3.2.1 The Precedence Shapley Value
4.3.2.2 The Hierarchical Solution
4.4 Power Measures for Digraphs and Solutions for Games with Hierarchies
4.4.1 Precedence Power Solutions for Games under Precedence Constraints
4.4.2 Power Measures, Solutions for Games with a Permission Structure and Permission Values
4.5 Logical Independence
4.5.1 Logical Independence of the Axioms in Theorem 4.5
4.5.2 Logical Independence of the Axioms in Theorem 4.7
4.6 Conclusions
4.7 Acknowledgments
Bibliography
5. Values, Nullifiers and Dummifiers
5.1 Introduction
5.2 Axiomatic Characterizations and Nullifying Players
5.3 The e-Banzhaf Value for TU-Games
5.4 Dummifying Players
5.5 The ie-Banzhaf Value for TU-Games
5.6 Conclusions
5.7 Acknowledgments
Bibliography
6. Games with Identical Shapley Values
6.1 Introduction
6.2 The Shapley Value
6.3 The Kernel of the Shapley Value
6.4 Axiomatizations of the Shapley Value Based on its Kernel
6.5 Bases for the Space of Games
6.6 Other Bases
6.7 Other Games in the Kernel of the Shapley Value
6.8 Proofs
6.9 Conclusions
6.10 Acknowledgments
Bibliography
7. Several Bases of a Game Space and an Application to the Shapley Value
7.1 Introduction
7.2 Notations and Definitions
7.3 Commander Games
7.4 Properties of Commander Games Basis
7.5 New Bases
7.6 Basis and Coincidence Condition
7.7 Conclusions
7.8 Acknowledgments
Bibliography
8. Extensions of the Shapley Value for Environments with Externalities
8.1 Introduction
8.2 The Environment
8.3 Axiomatic Extensions of the Shapley Value for Games with Externalities
8.4 Marginal Contributions
8.5 Other Approaches
8.5.1 The Potential Approach
8.5.2 The Harsanyi Dividends Approach
8.5.3 Algorithms
8.6 Non-Cooperative Approaches to Value Extensions
8.6.1 Implementation
8.6.2 A Bargaining Approach
8.7 Conclusions
8.8 Acknowledgments
Bibliography
9. The Shapley Value and other Values
9.1 Introduction
9.2 Preliminaries and Notation
9.3 Semivalues and Unanimity Games
9.4 Semivalues and Genetics
9.5 Semivalues and Social Choice
9.6 Conclusions
Bibliography
10. Power and the Shapley Value
10.1 Introduction
10.2 Preliminaries
10.3 Effectivity and Power
10.3.1 Finitely Many Alternatives
10.3.2 Infinitely Many Alternatives
10.3.2.1 An Application: The Owen-Shapley Spatial Power Index
10.4 Control and Power
10.5 Power on Digraphs
10.6 Conclusions
10.7 Acknowledgments
Bibliography
11. Cost Allocation with Variable Production and the Shapley Value
11.1 Introduction
11.2 Three Motivating Examples
11.2.1 The Tennessee Valley Authority
11.2.2 Internal Telephone Billing Rates
11.2.3 Aircraft Landing Fees
11.3 Notation and Preliminaries
11.4 The Classical Case and the Shapley-Shubik Method
11.4.1 Axiomatic Characterizations of the Shapley-Shubik Method
11.5 The Continuum Case and the Aumann-Shapley Method
11.5.1 Axiomatic Characterizations of the Aumann-Shapley Method
11.6 The Discrete Case and the Aumann-Shapley Method
11.6.1 Axiomatic Characterizations of the Discrete Aumann-Shapley Method
11.7 Conclusions
11.8 Acknowledgments
Bibliography
12. Pure Bargaining Problems and the Shapley Rule: A Survey
12.1 Introduction
12.2 Pure Bargaining Problems and Sharing Rules
12.3 Closures and Quasi-Additive Games
12.4 Core and the Shapley Rule
12.5 Axiomatic Characterizations of the Shapley Rule
12.5.1 Main Theorem
12.5.2 Other Domains
12.5.3 Discussing Monotonicity
12.6 Criticism on the Proportional Rule
12.6.1 Restricted Domain
12.6.2 Doubly Discriminatory Level
12.6.3 The Axiomatic Framework
12.6.4 Inconsistency: Cost-Saving Problems
12.6.5 Inconsistency: Added Costs Problems
12.7 Pure Bargaining Problems with a Coalition Structure
12.8 A Numerical Example
12.9 A General Result on Preferences
12.10 The Modified Shapley Rule and its Natural Domain
12.11 Conclusions
12.12 Suggestions
12.13 Acknowledgments
Bibliography
13. The Shapley Value as a Tool for Evaluating Groups: Axiomatization and Applications
13.1 Introduction
13.2 The Generalized Shapley Value: A Tool for Evaluating Groups
13.2.1 Profitability of a Group
13.3 Assessment of Groups in a Social Network
13.3.1 Myerson Group Value Decomposition: Communication and Betweenness
13.3.2 Communication and Betweenness Redundancy
13.4 Conclusions
13.5 Acknowledgments
Bibliography
14. A Value for j-Cooperative Games: Some Theoretical Aspects and Applications
14.1 Introduction
14.2 Some Motivating Examples
14.3 Preliminaries: j-Cooperative Games
14.4 A Value for j-Cooperative Games
14.5 Probabilistic Justification of the 𝓕-Value
14.6 The 𝓕-Value Restricted to Cooperative Games Is the Shapley Value
14.7 Another Formulation for the 𝓕-Value
14.8 Axiomatization
14.8.1 Classical Axioms for j-Cooperative Games
14.8.2 An Axiom on Unanimity Games
14.8.3 An Axiomatization for the 𝓕-Value
14.9 The 𝓕-Value on Constant-Sum j-Cooperative Games
14.10 Generating Functions for Computing the 𝓕-Value for Weighted j-Simple Games
14.11 Examples Revisited
14.12 Conclusions
14.13 Acknowledgments
Bibliography
15. The Shapley Value of Corporation Tax Games with Dual Benefactors
15.1 Introduction
15.2 Cost-Coalitional Problems with Multiple Dual and Irreplaceable Benefactors
15.3 Multiple Corporation Tax Games
15.4 The Shapley Value
15.5 An Example
15.6 Conclusions
15.7 Acknowledgments
Bibliography
16. The Shapley Value in Telecommunication Problems
16.1 Introduction
16.2 Some Uses of the Shapley Value in Mobile Communication Management
16.2.1 Resource Management in Wireless Networks
16.2.2 Channel Allocation in Mobile Communication Networks
16.2.3 Bandwidth Allocation in Heterogeneous Mobile Networks
16.2.4 Other Applications to Wireless Networks
16.3 The Shapley Value in Internet Problems
16.3.1 Keyword Auctions in Search Engines on Internet
16.3.2 Collaboration among ISPs
16.3.3 Some Additional Applications to Internet Problems
16.4 The Shapley Value in Communication Routing Problems
16.5 Conclusions
16.6 Acknowledgments
Bibliography
17. The Shapley Rule for Loss Allocation in Energy Transmission Networks
17.1 Introduction
17.2 The Model
17.2.1 The Mathematical Model
17.3 The Shapley Rule
17.4 Properties
17.4.1 Cost-Reflective Properties
17.4.2 Non-Discriminatory Properties
17.4.3 Properties to Foster Competition
17.5 Axiomatic Behavior of the Shapley Rule
17.6 Application to the Spanish Gas Transmission Network
17.6.1 Case Study with Real Data
17.6.2 Simulation Study Building upon the Real Data
17.7 Conclusions
17.8 Acknowledgments
Bibliography
18. On Some Applications of the Shapley-Shubik Index for Finance and Politics
18.1 Introduction
18.2 Some Preliminary Definitions
18.3 Short History
18.3.1 Power Indices Derived from Values
18.3.2 Autonomously Generated Power Indices
18.3.3 Some Other Indices with Different Derivations
18.4 Power Index Applications
18.5 Some Applications of Shapley-Shubik Power Index
18.5.1 Example of Financial Applications
18.5.2 Shares Shift between Two Shareholders
18.5.3 Trade of Shares between One Player and Ocean of Players
18.5.4 Remarks on Prices
18.5.5 Steadiness of Control
18.5.6 Indirect Control
18.5.7 Global Index of De-Stability
18.5.8 Portfolio Theory
18.6 Political Applications
18.6.1 Introduction
18.6.2 Simulations
18.6.3 Predictions
18.7 Conclusions
18.8 Acknowledgments
Bibliography
19. The Shapley Value in the Queueing Problem
19.1 Introduction
19.2 The Queueing Problem
19.3 The Shapley Value in the Optimistic Queueing Game
19.4 The Shapley Value in the Pessimistic Queueing Game
19.5 The Shapley Value in the Queueing Game with an Initial Order
19.6 Conclusions
19.7 Acknowledgments
Bibliography
20. Sometimes the Computation of the Shapley Value Is Simple
20.1 Introduction
20.2 Preliminaries
20.3 Games on a Linear Resource
20.3.1 Managing Airport Runways
20.3.2 Cleaning Rivers
20.3.3 Auctions and Markets
20.4 Decomposition
20.4.1 Sequencing Games
20.4.2 Maintenance Cost Games
20.4.3 Microarray Games and Network Centrality
20.4.4 Coverage Games
20.5 Conclusions
20.6 Acknowledgments
Bibliography
21. Analysing ISIS Zerkani Network Using the Shapley Value
21.1 Introduction
21.2 The Shapley Value
21.3 A New Game Theoretic Centrality Measure
21.4 Zerkani Network Analysis
21.5 Conclusions
21.6 Appendix
21.7 Acknowledgments
Bibliography
22. A Fuzzy Approach to Some Shapley Value Problems in Group Decision Making
22.1 Introduction
22.2 Preliminaries
22.2.1 Some Elements of the Theory of Fuzzy Sets
22.3 The Shapley Value for Majority Voting Games
22.4 Variability in the Quota q
22.5 Multi-Dimensional Descriptions of the Value of a Coalition
22.6 Discrepancy between the Weight and Shapley Value of a Player
22.7 Conclusions
Bibliography
23. Shapley Values for Two-Sided Assignment Markets
23.1 Introduction
23.2 The Shapley and Shubik Assignment Game
23.3 The Shapley Value of the Assignment Game
23.3.1 Balancedness Conditions
23.3.2 Axiomatic Characterization
23.4 The Shapley Value of a Related Market
23.4.1 Assignment Markets with Reservation Values
23.4.2 The Shapley Value of the Exact Assignment Game with the same Core
23.5 Conclusions
23.6 Acknowledgments
Bibliography
24. The Shapley Value in Minimum Cost Spanning Tree Problems
24.1 Introduction
24.2 Definitions
24.2.1 Cooperative Cost Games
24.2.2 Minimum Cost Spanning Tree Problems
24.3 Associated Cooperative Cost Games
24.3.1 The Private mcst Game
24.3.2 The Public mcst Game
24.3.3 The Optimistic mcst Game
24.3.4 Example
24.4 The Shapley Value
24.4.1 The Kar Solution
24.4.2 The Folk Solution
24.4.3 The Cycle-Complete Solution
24.5 Axiomatic Analysis
24.6 Correspondences with Other Concepts
24.6.1 Weighted Shapley Values
24.6.2 The Core and the Nucleolus
24.7 The Shapley Value in Other Related Problems

People also search for Handbook of the Shapley Value 1st:

handbook of the shapley value pdf
    
shapley value importance
    
handbook of the standard celeration chart
    
shapley value interpretation
    
the handy volume shakspeare

Tags:

Encarnacion Algaba,Vito Fragnelli,Joaquin Sanchez Soriano,Shapley Value