THEORY AND APPLICATIONS OF DYNAMIC GAMES : a course on noncooperative and cooperative games played... over event trees

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. "This is an excellent textbook on an important sub-area of dynamic games, viz., dynamic games over event trees. With its clarity of exposition and wealth of information, it is bound to draw many young researchers to this fascinating area and have a lasting impact." Vivek Borkar, Indian Institute of Technology Bombay, India "An advanced textbook on dynamic games played on event trees is long overdue. This book, written by leading experts in the field, will be of great use to modellers of economic behaviour under uncertainty. No doubt it will soon become a classic." Alain Haurie, University of Geneva, and GERAD/HEC Montreal "This book by Parilina, Reddy, and Zaccour provides a well-organized treatment of dynamic games on event trees under cooperative as well as noncooperative modes of play, constituting possibly the first such comprehensive study of this topic in text-book form." Tamer Basar, University of Illinois, USA Preface 6 Contents of the Book 7 Acknowledgements 9 Contents 10 Part I Static Games 13 1 Noncooperative Games 14 1.1 Finite Games in Strategic Form 14 1.1.1 Domination and Nash Equilibrium 16 1.2 Continuous Games in Strategic Form 19 1.2.1 Mixed Strategies 21 1.2.2 Existence of a Nash Equilibrium 22 1.2.3 Concave Games 24 1.3 Games in Extensive Form 30 1.3.1 Game Tree 30 1.3.2 Information Sets 31 1.3.3 Information Structure 33 1.3.4 Equilibrium in Behavior Strategies 34 1.3.5 Subgame Perfect Equilibrium 36 1.4 Stackelberg Equilibrium Solution 42 1.5 Additional Readings 46 1.6 Exercises 46 References 49 2 Cooperative Games 50 2.1 Elements of a Cooperative Game 50 2.2 Defining the Characteristic Function 54 2.3 Solutions to a Cooperative Game 57 2.3.1 The Core 58 2.3.2 The Shapley Value 61 2.4 The Nash Bargaining Solution 63 2.4.1 Price of Anarchy 68 2.5 Additional Readings 70 2.6 Exercises 71 References 73 Part II Deterministic Dynamic Games 75 3 Multistage Games 76 3.1 State-Space Description of Multistage Games 76 3.2 Information Structures 78 3.3 Strategies and Equilibrium Solutions 80 3.3.1 Open-Loop Nash Equilibrium 80 3.3.2 Feedback-Nash Equilibrium 82 3.4 Linear-Quadratic Multistage Games 87 3.4.1 Open-Loop Nash Equilibrium 88 3.4.2 Feedback-Nash Equilibrium 92 3.5 Additional Readings 95 3.6 Exercises 96 References 98 4 Sustainability of Cooperation in Dynamic Games 99 4.1 Dynamic Cooperative Games 99 4.1.1 Elements of the Game 100 4.2 Time-Consistent Solution 103 4.2.1 Imputation Distribution Procedure 105 4.2.2 An Example 109 4.3 Cooperative Equilibria 112 4.3.1 An Example 116 4.4 Incentive Equilibria 118 4.4.1 An Example 120 4.5 Additional Readings 125 4.5.1 Time Consistency 125 4.5.2 Cooperative Equilibria 126 4.5.3 Incentive Equilibria 127 4.6 Exercises 128 References 130 Part III Dynamic Games Played over Event Trees 134 5 Noncooperative Dynamic Games Played over Event Trees 135 5.1 Motivation 135 5.2 Event Tree as a Model of Uncertainty 136 5.3 Elements of a DGPET 138 5.4 S-adapted Nash Equilibrium 140 5.4.1 A Normal-Form Representation 140 5.5 The Maximum Principle 142 5.5.1 Node Consistency 143 5.6 Karush-Kuhn-Tucker Conditions and Equilibrium Formulation in DGPETs ... 145 5.7 An Example of a DGPET 146 5.8 DGPETs with Coupled Constraints 150 5.9 An Example of a DGPET with Coupled Constraints 155 5.10 DGPETs with Random Termination 160 5.10.1 Necessary Conditions 161 5.10.2 An Example of a DGPET with Random Termination 163 5.11 Additional Readings 166 5.12 Exercises 166 References 169 6 Node-Consistent Single-Valued Solutions in DGPETs 172 6.1 Cooperative DGPETs 172 6.2 Node Consistency of a Single-Valued Cooperative Solution 174 6.2.1 Node-Consistent Nash Bargaining Solution 177 6.2.2 Node-Consistent Shapley Value 179 6.3 Node-Consistent Shapley Value in DGPETs with Random Termination 180 6.3.1 Node-Consistent Shapley Value 182 6.3.2 An Example 186 6.4 Additional Readings 190 6.5 Exercises 192 References 194 7 Node-Consistent Core in DGPETs 196 7.1 Cooperative DGPETs 196 7.2 Node Consistency of the Core 198 7.3 The ε-Core and the Least Core 202 7.4 Example 207 7.5 Additional Readings 218 7.6 Exercises 220 References 225 8 Cooperative Equilibria in DGPETs 227 8.1 Preliminaries 227 8.2 Approximated Cooperative Equilibria in DGPETs 229 8.2.1 Cost of Cooperation in DGPETs 233 8.2.2 An Illustrative Example 234 8.3 Incentive Equilibrium Strategies in DGPETs 240 8.3.1 Linear-Quadratic DGPET 240 8.3.2 Cooperative Solution 241 8.3.3 S-adapted Incentive Equilibria 244 8.3.4 An Example 248 8.4 Additional Readings 253 8.5 Exercises 256 References 258 Index 261