This contributed volume presents the state-of-the-art of games and dynamic games, featuring several chapters based on plenary sessions at the ISDG-China Chapter Conference on Dynamic Games and Game Theoretic Analysis, which was held from August 3-5, 2017 at the Ningbo campus of the University of Nottingham, China. The chapters in this volume will provide readers with paths to further research, serving as a testimony to the vitality of the field. Experts cover a range of theory and applications related to games and dynamic games, with topics including:
Dynamically stable cooperative provision of public goods under non-transferable utility
Strongly time-consistent solutions in cooperative dynamic games
Incentive Stackelberg games for stochastic systems
Static and inverse Stackelberg games in political economy
Cournot and Betrand competition on symmetric R&D networks
Numerical Nash equilibria using curvilinear multistart algorithm
Markov chain approximation numerical scheme for infinite-horizon mean field games
Frontiers in Games and Dynamic Games will appeal to an interdisciplinary audience of researchers, practitioners, and graduate students interested in games and dynamic games.
Author(s): David Yeung, Shravan Luckraz, Chee Kian Leong
Series: Annals of the International Society of Dynamic Games
Edition: 2
Publisher: Springer Nature
Year: 2020
Language: English
Pages: 243
City: Switzerland AG
Tags: Game theory Dynamic Games Dynamic games game theory Dynamic games and applications ISDG-China Game theoretic Analysis Game theory books Market failure Differential gamesDynamic Cooperative Games Stackelberg game Non zero sum games Mean field games Noncooperative Game Theory Auction and Mechanism Design
Preface
References
Acknowledgments
Contents
Contributors
Part I Cooperative Dynamic Games (Plenary Lectures)
Dynamically Stable Cooperative Provision of Public Goods Under Non-transferable Utility
1 Introduction
2 Theoretical Framework of Public Goods Provision
2.1 Pareto Optimality and Individual Rationality under Cooperation
2.2 The Core and Dynamically Stable Subcore
2.3 Dynamically Stable Subcore with Variable Weights
3 An NTU Differential Game of Public Goods Provision
4 Cooperative Scheme: Constant Payoff Weight Case
4.1 Optimal Cooperative Trajectories
4.2 Individual Payoff Under Cooperation
4.3 Dynamically Stable Core
5 Variable Payoff Weights Scheme
6 Concluding Remarks
A.1 Proof of Proposition 3.1
B.1 Proof of Proposition 4.1
C.1 Proof of Proposition 4.3
References
Strongly Time-Consistent Solutions in CooperativeDynamic Games
1 What Is Strongly Time-Consistency?
1.1 Cooperative Differential Game
1.2 Transformation of Characteristic Function
2 Repeated Games
2.1 Associated Zero-Sum Games
2.2 Multistage Games
2.3 Time-Consistency and Strongly Time-Consistency
References
Part II Stackelberg Games
Incentive Stackelberg Games for Stochastic Systems
1 Introduction
2 The Basic Concept of Incentive Stackelberg Game
3 Incentive Stackelberg Game with One Leader and Multiple Followers
3.1 Definitions and Preliminaries
3.2 Problem Formulation
3.3 Main Results
3.4 Infinite-Horizon Case
3.5 Numerical Example
4 Incentive Stackelberg Games for a Class of Markovian Jump Linear Stochastic Systems
4.1 Preliminary Results
4.2 Problem Formulation
4.3 Main Results
4.4 Leader's Nash Equilibrium Strategy
4.5 Follower's Nash Equilibrium Strategy
4.6 Follower's Pareto Optimal Strategy
4.7 Numerical Example
4.8 Incentive Possibility
5 Static Output Feedback Case
5.1 Preliminary Results
5.2 Problem Formulation
5.3 Main Results
5.3.1 Leader's Pareto Optimal Strategy
5.3.2 Follower's Pareto Optimal Strategy
6 Incentive Stackelberg Strategy for Stochastic LPV Systems
6.1 Preliminary Results
6.2 Problem Formulation
6.3 Main Results
6.4 Numerical Algorithm for Solving CCMIs
6.5 Numerical Example
7 Conclusion
References
Social and Private Interests Coordination Engines in Resource Allocation: System Compatibility, Corruption, and Regional Development
1 Introduction
2 SPICE-Models and Conditions of System Compatibility
2.1 SPICE-Models with Two Agents
2.1.1 Independence
2.1.2 Hierarchy
2.1.3 Cooperation
2.2 SPICE-Models with Several Agents
3 Control Mechanisms of System Compatibility
3.1 Economic Mechanisms
3.2 Administrative Mechanisms
4 Corruption in SPICE-Models
4.1 Economic Corruption in SPICE-Models
4.2 Administrative Corruption in SPICE-Models
5 SPICE-Models in the Regional Development
5.1 Administrative Control Mechanisms
5.2 Economic Control Mechanisms
5.3 Mechanisms of Resource Allocation
6 Conclusion
References
Part III Games on Graphs and Networks
A Multi-Stage Model of Searching for Two Mobile Objectson a Graph
1 Problem Statement and Notation
2 Single-Stage Game
3 Multi-stage Game
4 Existence of Equilibrium
5 Solution for a Single-Stage Game
6 Solution of the Game for a Linear Graph
7 Solution for a Two-Stage Game
8 Solution for a Multi-stage Game
9 Solution for a Single-Stage Game with an Arbitrary Detection Probability
References
The Impact of Product Differentiation on Symmetric R&D Networks
1 Introduction
2 The Model
3 Cournot Competition
4 Bertrand Competition
5 Comparison of Cournot and Bertrand Equilibria
6 Conclusion
Appendix 1
Proof of Lemma 1
Proof of Lemma 2
Proof of Proposition 1
Proof of Proposition 2
Proof of Proposition 3
Proof of Proposition 4
Proof of Proposition 3
Proof of Proposition 9
Appendix 2
References
Part IV Numerical Methods in Games and Dynamic Games
A Global Optimization Approach to Nonzero Sum Six-Person Game
1 Introduction
2 Nonzero Sum n-Person Game
3 The Curvilinear Multistart Algorithm
4 Computational Experiments
References
An Infinite-Horizon Mean Field Game of Growth and Capital Accumulation: A Markov Chain Approximation Numerical Scheme and Its Challenges
1 Introduction
2 Mean Field Games of Growth and Capital Accumulation
3 Solution
4 Markov Chain Approximation Scheme
5 Concluding Remarks
References
