This textbook provides a comprehensive overview of noncooperative and cooperative dynamic games involving uncertain parameter values, with the stochastic process being described by an event tree. Primarily intended for graduate students of economics, management science and engineering, the book is self-contained, as it defines and illustrates all relevant concepts originally introduced in static games before extending them to a dynamic framework. It subsequently addresses the sustainability of cooperative contracts over time and introduces a range of mechanisms to help avoid such agreements breaking down before reaching maturity. To illustrate the concepts discussed, the book provides various examples of how dynamic games played over event trees can be applied to environmental economics, management science, and engineering.
Author(s): Elena Parilina, Puduru Viswanadha Reddy, Georges Zaccour
Series: Theory and Decision Library C, 51
Publisher: Springer
Year: 2022
Language: English
Pages: 262
City: Cham
Preface
Contents of the Book
Acknowledgements
Contents
Part I Static Games
1 Noncooperative Games
1.1 Finite Games in Strategic Form
1.1.1 Domination and Nash Equilibrium
1.2 Continuous Games in Strategic Form
1.2.1 Mixed Strategies
1.2.2 Existence of a Nash Equilibrium
1.2.3 Concave Games
1.3 Games in Extensive Form
1.3.1 Game Tree
1.3.2 Information Sets
1.3.3 Information Structure
1.3.4 Equilibrium in Behavior Strategies
1.3.5 Subgame Perfect Equilibrium
1.4 Stackelberg Equilibrium Solution
1.5 Additional Readings
1.6 Exercises
References
2 Cooperative Games
2.1 Elements of a Cooperative Game
2.2 Defining the Characteristic Function
2.3 Solutions to a Cooperative Game
2.3.1 The Core
2.3.2 The Shapley Value
2.4 The Nash Bargaining Solution
2.4.1 Price of Anarchy
2.5 Additional Readings
2.6 Exercises
References
Part II Deterministic Dynamic Games
3 Multistage Games
3.1 State-Space Description of Multistage Games
3.2 Information Structures
3.3 Strategies and Equilibrium Solutions
3.3.1 Open-Loop Nash Equilibrium
3.3.2 Feedback-Nash Equilibrium
3.4 Linear-Quadratic Multistage Games
3.4.1 Open-Loop Nash Equilibrium
3.4.2 Feedback-Nash Equilibrium
3.5 Additional Readings
3.6 Exercises
References
4 Sustainability of Cooperation in Dynamic Games
4.1 Dynamic Cooperative Games
4.1.1 Elements of the Game
4.2 Time-Consistent Solution
4.2.1 Imputation Distribution Procedure
4.2.2 An Example
4.3 Cooperative Equilibria
4.3.1 An Example
4.4 Incentive Equilibria
4.4.1 An Example
4.5 Additional Readings
4.5.1 Time Consistency
4.5.2 Cooperative Equilibria
4.5.3 Incentive Equilibria
4.6 Exercises
References
Part III Dynamic Games Played over Event Trees
5 Noncooperative Dynamic Games Played over Event Trees
5.1 Motivation
5.2 Event Tree as a Model of Uncertainty
5.3 Elements of a DGPET
5.4 S-adapted Nash Equilibrium
5.4.1 A Normal-Form Representation
5.5 The Maximum Principle
5.5.1 Node Consistency
5.6 Karush-Kuhn-Tucker Conditions and Equilibrium Formulation in DGPETs …
5.7 An Example of a DGPET
5.8 DGPETs with Coupled Constraints
5.9 An Example of a DGPET with Coupled Constraints
5.10 DGPETs with Random Termination
5.10.1 Necessary Conditions
5.10.2 An Example of a DGPET with Random Termination
5.11 Additional Readings
5.12 Exercises
References
6 Node-Consistent Single-Valued Solutions in DGPETs
6.1 Cooperative DGPETs
6.2 Node Consistency of a Single-Valued Cooperative Solution
6.2.1 Node-Consistent Nash Bargaining Solution
6.2.2 Node-Consistent Shapley Value
6.3 Node-Consistent Shapley Value in DGPETs with Random Termination
6.3.1 Node-Consistent Shapley Value
6.3.2 An Example
6.4 Additional Readings
6.5 Exercises
References
7 Node-Consistent Core in DGPETs
7.1 Cooperative DGPETs
7.2 Node Consistency of the Core
7.3 The ε-Core and the Least Core
7.4 Example
7.5 Additional Readings
7.6 Exercises
References
8 Cooperative Equilibria in DGPETs
8.1 Preliminaries
8.2 Approximated Cooperative Equilibria in DGPETs
8.2.1 Cost of Cooperation in DGPETs
8.2.2 An Illustrative Example
8.3 Incentive Equilibrium Strategies in DGPETs
8.3.1 Linear-Quadratic DGPET
8.3.2 Cooperative Solution
8.3.3 S-adapted Incentive Equilibria
8.3.4 An Example
8.4 Additional Readings
8.5 Exercises
References
Index
