This is a collection of recent novel contributions in game theory from a group of prominent authors in the field. It covers Non-cooperative Games, Equilibrium Analysis, Cooperative Games and Axiomatic Values in static and dynamic contexts.
Part 1: Non-cooperative Games and Equilibrium Analysis
In game theory, a non-cooperative game is a game with competition between individual players and in which only self-enforcing (e.g. through credible threats) alliances (or competition between groups of players, called "coalitions") are possible due to the absence of external means to enforce cooperative behavior (e.g. contract law), as opposed to cooperative games. In fact, non-cooperative games are the foundation for the development of cooperative games by acting as the status quo. Non-cooperative games are generally analysed through the framework of equilibrium, which tries to predict players' individual strategies and payoffs. Indeed, equilibrium analysis is the centre of non-cooperative games. This volume on non-cooperative games and equilibrium analysis contains a variety of non-cooperative games and non-cooperative game equilibria from prominent authors in the field.
Part 2: Cooperative Games and Axiomatic Values
It is well known that non-cooperative behaviours, in general, would not lead to a Pareto optimal outcome. Highly undesirable outcomes (like the prisoner's dilemma) and even devastating results (like the tragedy of the commons) could appear when the involved parties only care about their individual interests in a non-cooperative situation. Cooperative games offer the possibility of obtaining socially optimal and group efficient solutions to decision problems involving strategic actions. In addition, axiomatic values serve as guidance for establishing cooperative solutions. This volume on cooperative games and axiomatic values presents a collection of cooperative games and axiomatic values from prominent authors in the field.
Author(s): Leon A Petrosyan (editor), David Wing Kay Yeung (editor)
Publisher: WSPC
Year: 2019
Language: English
Pages: 622
Contents
List of Contributors
About the Editors
1. Introduction
Part I. Non-Cooperative Games and Equilibrium Analysis
2. On Pure-Strategy Nash Equilibria in a Duopolistic Market Share Model
1. Introduction
2. Results
3. Modeling Background
4. Our Advertising Model
4.1. Advertising games with low costs
5. Existence of a Strict Nash Equilibrium in Pure Strategies
6. Market Shares at Equilibrium for an Asymmetric Advertising Situation
7. Conclusions, Limitations and Future Work
Appendix A. Proofs
Acknowledgments
References
3. Maximin and Minimax Strategies in Two-Players Game with Two Strategic Variables
1. Introduction
2. The Model
3. Maximin and Minimax Strategies
3.1. x-game
3.1.1. Maximin strategy
3.2. p-game
4. Special Case
5. Mixed Game
6. Maximization of Weighted Average of Absolute and Relative Profits in an Duopoly
7. Concluding Remark
Acknowledgments
References
4. Noncooperative Dynamic Contribution to a Public Project
1. Introduction
2. The Model
3. Optimal Policy
4. Markov-perfect Nash Equilibrium
5. Closed Forms
6. Comparison
7. Conclusion
Acknowledgment
Appendix A
A.1. Comparative statics: Cooperative solution
A.2. Comparative statics: Noncooperative solution
References
5. Infinite Horizon Dynamic Games: A New Approach via Information Updating
1. Introduction
2. Game Formulation and Equilibrium
3. Information Updating
4. An Illustration in Resource Extraction
4.1. Game equilibrium
4.2. Comparison with standard infinite horizon games
5. Conclusions
Appendix A. Proof of Theorem 2.1
Appendix B. Proof of Proposition 4.1
References
6. Contracts and Information Structure in a Supply Chain with Operations and Marketing Interaction
1. Introduction
2. Differential Game Model
3. Open-loop Nash Equilibrium Strategies
4. Feedback Nash Equilibrium Strategies
5. Comparisons of Contracts and Strategies
5.1. Optimal contracts and strategies
5.2. Optimal operations and marketing policies
6. Conclusions
Appendix A
A.1 Appendix
A.2 Appendix
A.3 Appendix
A.4 Appendix
A.5 Appendix
A.6 Appendix
A.7 Appendix
A.8 Appendix
Acknowledgments
References
7. Equilibrium Prices and Flows in the Passenger Traffic Problem
1. Introduction
2. Game-Theoretic Model
3. Transport Game on Two Parallel Routes with the Linear Latency Function
4. Transport Game on N Parallel Channels with the Linear Latency Function
5. Transport Game with the Nonlinear Latency Function
5.1. Transport game on two parallel routes
5.2. Transport game on n parallel routes with the nonlinear latency function
6. Transport Game on Euler Graph
7. Conclusion
Acknowledgments
References
8. Existence of Unique Equilibrium in Cournot Mixed Oligopoly
1. Introduction
2. Model and Analysis
3. Conclusion
Acknowledgment
References
9. Second-Price All-Pay Auctions and Best-Reply Matching Equilibria
1. Introduction
2. Classroom Experiments, NE and Students’ Behavior
3. Philosophy of Mixed NE and Philosophy of BRM
4. BRM and Students’ Way of Playing
5. GBRM, Focal Values and Focal Behavior, a Way to Bring Closer First-Price and Second-Price All-Pay Auctions
6. BRME, GBRME, NE and Payoffs
7. Concluding Remarks
Acknowledgments
Appendix A: Proof of Result 1 (Umbhauer [2017])
Appendix B: Proof of Result 2
Appendix C: Proof of Proposition 1
Appendix D: Proof of Proposition 2
Appendix E: Proof of Proposition 3
E.1. First part of the proposition
E.2. Second part of the proposition
Appendix F: Proof of Proposition 4
Appendix G: Proof of Proposition 5
References
10. Cournot Equilibrium Uniqueness: At 0 Discontinuous Industry Revenue and Decreasing Price Flexibility
1. Introduction
2. Setting and Various Fundamental Objects
2.1. Setting
2.2. Marginal reductions
2.3. Virtual backward reply functions
3. Main Result
4. The Selten–Szidarovszky Technique: A Basic Result
5. Proof of Theorem 2
5.1. Observations on assumptions
5.2. Proof
6. Algorithm
7. Concluding Remarks
Acknowledgment
References
11. Quantifying Commitment in Nash Equilibria
1. Introduction
1.1. Literature
1.2. Outline
2. Models
2.1. Normal-form game
2.2. Canonical extension
3. Sequential Implementation
4. A Measure of Commitment
5. Conclusion
Acknowledgments
References
12. Equilibria in Dynamic Multicriteria Games
1. Introduction
2. Multicriteria Games and Solution Concepts
3. Multicriteria Dynamic Game and Multicriteria Nash Equilibrium
4. Dynamic Multicriteria Model with Infinite Horizon
4.1. The guaranteed payoffs and multicriteria Nash equilibrium: Variant 1
4.2. The guaranteed payoffs and multicriteria Nash equilibrium: Variant 2
4.3. The guaranteed payoffs and multicriteria Nash equilibrium: Variant 3
4.4. Comparison and numerical experiments
5. Dynamic Multicriteria Model with Random Harvesting Times
Appendix A
Appendix B. Proof of Theorem 1
Acknowledgments
References
13. Economic Problems with Constraints: How Efficiency Relates to Equilibrium
1. Introduction
2. A Constrained Efficient Solution or Game Equilibrium?
3. Existence and Uniqueness of CCE
4. The Relationship Between Pareto-Efficient Solutions and Rosen’s Equilibria
4.1. A two-player game
4.1.1. Pareto-efficiency and Rosen’s equilibrium first-order conditions
4.1.2. Relations between α and r
4.2. Oligopoly
5. Realization of Public Good Delivery
5.1. A public good delivery model
5.2. Regulator’s solution
5.3. Which CCE are available
6. Concluding Remarks
Acknowledgments
Appendix A. Rosen’s Relative Weights in R2+
References
14. Substitution, Complementarity, and Stability
1. Introduction
2. Results
2.1. Model
2.2. Substitution
2.3. Complementarity
3. Discussion
Acknowledgments
References
Part II. Cooperative Games and Axiomatic Values
15. On Analyzing Cost Allocation Problems: Cooperation Building Structures and Order Problem Representations
1. Introduction
2. Cooperation Building Structures
3. Sequencing Situations Without Initial Order
4. Maintenance Problems
5. Minimum Cost Spanning Tree Situations
6. Permutation Situations Without Initial Allocation
7. Public Congestion Network Situations
7.1. Convex congestion network situations
7.2. Concave congestion network situations
8. Traveling Salesman and Related Problems
8.1. Traveling salesman problems
8.2. Shared taxi problems
8.3. Traveling repairman problems
References
16. Coalition Formation with Externalities: The Case of the Northeast Atlantic Mackerel Fishery in a Pre- and Post-Brexit Context
1. Introduction
2. Bioeconomic Model
2.1. Cooperative management
2.2. Noncooperative management
3. Game Theoretic Model
3.1. Second stage of coalition formation
3.2. First stage of coalition formation
4. Empirical Model
4.1. Stock–recruitment relationship
4.2. Share of mackerel stock
4.3. Unit cost of harvest
5. Numerical Results and Discussion
6. Conclusion
Acknowledgments
Appendix A
A.1. Proof of noncooperative “golden-rule”
A.2. Illustration of coalition structure stability concepts
References
17. Stable Marketing Cooperation in a Differential Game for an Oligopoly
1. Introduction
2. The Model
3. Random Terminal Time
4. Noncooperative Game
5. Cooperative Game
6. Stability of Cooperation
7. Concluding Remarks
Acknowledgments
References
18. A Cooperative Dynamic Environmental Game of Subgame Consistent Clean Technology Development
1. Introduction
2. Game Formulation
2.1. Clean technology development
2.2. Impacts and accumulation dynamics of pollutants
2.3. Industry equilibria and nations’ objectives
3. Noncooperative Outcomes
4. Cooperative Clean Technology Developmen tand Pollution Control
4.1. Gains in cooperative clean technique development
4.2. Cooperative optimization
4.3. Subgame consistent collaboration
5. Imputation Distribution Mechanism
6. Conclusions
Appendix A. Proof of Theorem 3.1
Appendix B. Proof of Proposition 3.1
References
19. Partnership’s Profit Sharing: Linear and Nonlinear Contracts
1. Introduction
2. Model and Optimality Conditions
3. Analysis of the Model
4. Constrained Model
5. Partners’ Shares Grow Linearly
6. Identical Beliefs of the Partners
7. Risk Neutral Partners
8. Conclusions
Appendix: The Stories
References
20. Stackelberg Oligopoly TU-Games: Characterization and Nonemptiness of the Core
1. Introduction
2. The Model
2.1. TU-games
2.2. Strategic Stackelberg oligopoly games
2.3. Towards Stackelberg oligopoly TU-games
3. Core Results
3.1. Characterization of the core
3.2. Nonemptiness of the core
4. Concluding Remarks
Acknowledgments
References
21. Strong Strategic Support of Cooperation in Multistage Games
1. Introduction
2. Repeated Games
2.1. Game description
2.2. Associated zero-sum games
3. Multistage Games
3.1. Game description
3.2. Associated zero-sum games
Acknowledgment
References
22. A Solution Concept Related to “Bounded Rationality” for Some Two-Echelon Models
1. Introduction
2. Literature Review
3. On 2-Games Arising from Two-Sided Transportation Situations
4. A Catcher of the Core
5. Bounded Rationality and Numerical Study
6. Conclusions
Acknowledgments
References
23. Intrinsic Comparative Statics of a Nash Bargaining Solution
1. Introduction
2. Preliminaries
3. Intrinsic Qualitative Properties
4. Summary and Conclusion
References
24. Optimal Fair Division for Measures with Piecewise Linear Density Functions
1. Introduction
2. The Main Result
3. Final Remarks
Acknowledgment
References
25. An Extension of the Solidarity Value for Environments with Externalities
1. Introduction
2. Framework and Conventions
3. The Axioms
4. Characterization
5. A Comment on Related Literature
Acknowledgment
References
26. On Harsanyi Dividends and Asymmetric Values
1. Introduction
2. Transferable Utility Games
2.1. Characteristic functions
2.2. Superadditivity and monotonicity
2.3. Harsanyi dividends
2.4. Positive games
2.5. Marginal contributions
2.6. Convex games
3. Values and Solution Sets
3.1. Basic properties
3.2. Imputations
3.3. Stable allocations: The core
3.4. Quasi-values and random order values: The Weber set
3.5. Dividend distributions: The Harsanyi set
3.6. Weighted Shapley values
3.7. Relation between solutions
4. Characterizing Solutions
4.1. Characterization by axioms
4.2. Characterization by restrictions on dividend distributions
4.3. Implications of monotonic dividend distributions
4.4. Graph structures and restrictions on dividend distributions
4.5. An illustration: Liability games
5. Concluding Remarks
Appendix A
Acknowledgments
References
27. An Axiomatization for Two Power Indices for (3,2)-Simple Games
1. Introduction
2. Preliminaries and Definitions
3. Axioms for Power Indices for (3,2)-Simple Games
3.1. Classical axioms for (3, 2)-simple games
3.2. A new axiom for the Shapley–Shubik index for (3, 2)-simple games
4. The Characterization of the Shapley–Shubik Index for (3,2)-Simple Games
4.1. Independence of the axiom for the Shapley–Shubik power index for (3, 2)-simple games
5. A Similar Approach for the Banzhaf Index for (3,2)-Simple Games
5.1. Characterization of the Banzhaf index for (3, 2)-simple games
5.2. Independence of the axiom for the Banzhaf index for (3, 2)-simple games
6. Conclusion
Acknowledgments
References
28. Indices of Criticality in Simple Games
1. Introduction
2. Preliminaries
3. Indices of Criticality
4. Monotonicity Properties for Weighted Majority Games
5. First Steps Toward a Characterization
6. Examples
7. Conclusions
Acknowledgments
References
Index
