Pareto-Nash-Stackelberg Game and Control Theory

This book presents a comprehensive new, multi-objective and integrative view on traditional game and control theories. Consisting of 15 chapters, it is divided into three parts covering noncooperative games; mixtures of simultaneous and sequential multi-objective games; and multi-agent control of Pareto-Nash-Stackelberg-type games respectively. Can multicriteria optimization, game theory and optimal control be integrated into a unique theory? Are there mathematical models and solution concepts that could constitute the basis of a new paradigm? Is there a common approach and method to solve emerging problems? The book addresses these and other related questions and problems to create the foundation for the Pareto-Nash-Stackelberg Game and Control Theory. It considers a series of simultaneous/Nash and sequential/Stackelberg games, single-criterion and multicriteria/Pareto games, combining Nash and Stackelberg game concepts and Pareto optimization, as well as a range of notions relatedto system control. In addition, it considers the problems of finding and representing the entire set of solutions. Intended for researches, professors, specialists, and students in the areas of game theory, operational research, applied mathematics, economics, computer science and engineering, it also serves as a textbook for various courses in these fields.

Inhalt

1. Introduction

Part I Noncooperative Games

2. Nash Equilibrium Conditions As Extensions Of Some Classical Optimisation Theorems 3. Sets Of Nash Equilibria In Polymatrix Mixed-Strategy Games 4. Sets Of Nash Equilibria In Bimatrix 2 × 3 Mixed-Strategy Games

5. Nash Equilibrium Sets In Dyadic Trimatrix Mixed-Strategy Games

6. Nash Equilibrium Set Function In Dyadic Mixed-Strategy Games

7. Stackelberg Equilibrium Sets In Polymatrix Mixed-Strategy Generalized Stackelberg Games 8. Strategic Form Games On Digraphs Part II Mixtures of Simultaneous And Sequential Games

9. Solution Principles For Mixtures Of Simultaneous And Sequential Games 10. Computing Pareto-Nash Equilibrium Sets In Finite Multi-Objective Mixed-Strategy Games 11. Sets Of Pareto-Nash Equilibria In Dyadic Two-Criterion Mixed-Strategy Games

12. Taxonomy Of Strategic Games With Information Leaks And Corruption Of Simultaneity

Part III Pareto-Nash-Stackelberg Game And Control Processes

13. Linear Discrete-Time Pareto-Nash-Stackelberg Control And Its Principles

14. Linear Discrete-Time Set-Valued Pareto-Nash-Stackelberg Control And Its Principles

15. Linear Discrete Pareto-Nash-Stackelberg Control Processes Withechoes And Retroactive Future