Pareto-Nash-Stackelberg Game and Control Theory: Intelligent Paradigms and Applications (Smart Innovation, Systems and Technologies)

Preface
Contents
Symbols & Abbreviations
1 Introduction
	1.1 Basic Preliminary Terminology
		1.1.1 Conflict and Cooperation Notions
		1.1.2 What is Game Theory?
		1.1.3 Decision Making
		1.1.4 Multi-Objective Optimization
		1.1.5 Multi-Agent Decision Problems
		1.1.6 Decision Making Problems in Situations of Risk
		1.1.7 Decision Making Problems Under Uncertainty
		1.1.8 Pascal's Wager
		1.1.9 Standard Decision Theory Versus Game Theory
		1.1.10 Strategy Notion
		1.1.11 Brief History of Game Theory and Optimal Control
	1.2 Game Theory Branches. General and Particular Models. Solution Concepts
		1.2.1 Branches. General Models. Solution Concepts
		1.2.2 Prisoner's Dilemma
		1.2.3 To Cooperate or Not To Cooperate?
		1.2.4 Coordination Games
		1.2.5 Anti-Coordination Games
		1.2.6 Antagonistic Games
		1.2.7 Game Modelling and Solution Concepts
	1.3 Strategic Form Games
	1.4 Simultaneous/Nash Games
	1.5 Sequential/Stackelberg Games
	1.6 Optimal Control Theory
	1.7 Applications
	1.8 Game Theorists and Nobel Memorial Prize  in Economic Sciences
	1.9 Objectives and Outline
	References
--- Noncooperative Games
2 Nash Equilibrium Conditions as Extensions of Some Classical Optimisation Theorems
	2.1 Introduction
	2.2 The Saddle Point and the Nash Equilibrium General Sufficient Condition
	2.3 Necessary and Sufficient Conditions for Convex Strategic Games
	2.4 Equilibrium Principles and Conditions for Multi-criteria Strategic Games
	2.5 Conclusions
	References
3 Sets of Nash Equilibria in Polymatrix Mixed-Strategy Games
	3.1 Introduction
	3.2 Nash Equilibrium Sets in Bimatrix Mixed-Strategy Games
		3.2.1 Algorithm for Nash Equilibrium Sets Computing  in Bimatrix Games
		3.2.2 Examples of Nash Equilibrium Sets Computing  in Bimatrix Games
	3.3 Nash Equilibrium Sets in Polymatrix Mixed-Strategy Games
		3.3.1 Algorithm for Nash Equilibrium Sets Computing in Polymatrix Mixed-Strategy Games
	3.4 Conclusions
	References
Sets of Nash Equilibria in Bimatrix 2×3 Mixed-Strategy Games
	4.1 Introduction
	4.2 Main Results
		4.2.1 Games on a Triangular Prism
		4.2.2 Both Players Have Either Equivalent Strategies or Dominant Strategies
		4.2.3 One Player Has Dominant Strategy
		4.2.4 One Player Has Equivalent Strategies
		4.2.5 Players Don't Have Dominant Strategies
	4.3 Algorithm for Constructing the Set of Nash Equilibria
	4.4 Conclusions
	References
5 Nash Equilibrium Sets in Dyadic Trimatrix Mixed-Strategy Games
	5.1 Introduction
	5.2 Main Results
		5.2.1 Games on a Unit Cube
		5.2.2 All Players Have Either Equivalent or Dominant Strategies
		5.2.3 Two Players Have Dominant or Equivalent Strategies
		5.2.4 Every Player Has Different Types of Strategies: Dominant, Equivalent, or Incomparable
		5.2.5 Two Players Have Either Incomparable or Equivalent Strategies
		5.2.6 All Players Have Incomparable Strategies
	5.3 Algorithm
	5.4 Conclusions
	References
6 Nash Equilibrium Set Function in Dyadic Mixed-Strategy Games
	6.1 Game Statement and Its Simplification
	6.2 Optimal Value Functions and Best Response Mappings
	6.3 Nash Equilibria and Nash Equilibrium Set Function
	6.4 Conclusions
	References
7 Stackelberg Equilibrium Sets in Polymatrix Mixed-Strategy Generalized Stackelberg Games
	7.1 Introduction
	7.2 Stackelberg Equilibrium Sets in Bimatrix Mixed-Strategy Stackelberg Games
	7.3 Polynomial Algorithm for a Single Stackelberg …
	7.4 Stackelberg Equilibrium Sets in Polymatrix Mixed-Strategy Games
	7.5 Conclusions
	References
8 Strategic Form Games on Digraphs
	8.1 Introduction
	8.2 Matrix Games on Digraphs
		8.2.1 Concepts
		8.2.2 Properties of Digraph Matrix Games
	8.3 Solvable Matrix Games on Digraphs
		8.3.1 Maximin Directed Tree
		8.3.2 Maximin Directed Path
		8.3.3 Maximin Traveling Salesman Problem with Transportation
		8.3.4 Maximin Cost Flow
	8.4 Polymatrix Games on Digraphs
	8.5 Dynamic Games on Digraphs
	8.6 Concluding Remarks
	References
--- Mixtures of Simultaneous & Sequential Games
9 Solution Principles for Mixtures  of Simultaneous & Sequential Games
	9.1 Introduction
	9.2 Unsafe Stackelberg Equilibria. Existence  and Properties
	9.3 Safe Stackelberg Equilibria
	9.4 Pseudo-Equilibria. Nash-Stackelberg Equilibria
	9.5 Multi-objective Pseudo-Equilibria. Pareto-Nash-Stackelberg Equilibria
	9.6 Concluding Remarks
	References
10 Computing Pareto–Nash Equilibrium Sets in Finite Multi-Objective Mixed-Strategy Games
	10.1 Introduction
	10.2 Pareto Optimality
	10.3 Pareto–Nash Equilibria
	10.4 Scalarization Technique
	10.5 Pareto–Nash Equilibrium Set in Two-Player Mixed-Strategy Games
	10.6 Pareto–Nash Equilibrium Sets in Multi-Criterion Polymatrix Mixed-Strategy Games
	10.7 Conclusions
	References
11 Sets of Pareto–Nash Equilibria in Dyadic Two-Criterion Mixed-Strategy Games
	11.1 Introduction
	11.2 Pareto Optimality
	11.3 Synthesis Function
	11.4 Pareto–Nash Equilibrium
	11.5 Dyadic Two-Criterion Mixed-Strategy Games
	11.6 The Wolfram Language Program
	11.7 Concluding Remarks
	References
12 Taxonomy of Strategic Games with Information Leaks & Corruption of Simultaneity
	12.1 Introduction
		12.1.1 Normal Form Game and Axioms
		12.1.2 Axiom of Simultaneity and Its Corruption
		12.1.3 Theory of Moves
	12.2 Taxonomy of Bimatrix Games with Information Leaks
		12.2.1 Knowledge and Types of Games
		12.2.2 Taxonomy Elements
	12.3 Solution Principles for Bimatrix Games with Information Leak …
		12.3.1 Nash Taxon
		12.3.2 Stackelberg Taxon
		12.3.3 Maximin Taxon
		12.3.4 Maximin-Nash Taxon
		12.3.5 Optimum Taxon
		12.3.6 Optimum-Nash Taxon
		12.3.7 Optimum-Stackelberg Taxon
	12.4 Taxonomy of Bimatrix Games with Information Leak and More Than Two Levels of Knowledge
	12.5 Repeated Bimatrix Games with Information Leaks
	12.6 Taxonomy of Polymatrix Games with Information Leaks and More Than Two Levels of Knowledge
	12.7 Conclusions
	References
--- Pareto-Nash-Stackelberg Game & Control Processes
13 Linear Discrete-Time Pareto-Nash-Stackelberg Control & its Principles
	13.1 Introduction
	13.2 Linear Discrete-Time Optimal Control Problem
	13.3 Linear Discrete-Time Stackelberg Control Problem
	13.4 Linear Discrete-Time Pareto-Stackelberg Control Problem
	13.5 Linear Discrete-Time Nash-Stackelberg Control Problem
	13.6 Linear Discrete-Time Pareto-Nash-Stackelberg Control Problem
	13.7 Linear Discrete-Time Set-Valued Optimal Control Problem
	13.8 Concluding Remarks
	References
14 Linear Discrete-Time Set-valued Pareto-Nash-Stackelberg Control & its Principles
	14.1 Introduction
	14.2 Linear Discrete-Time Set-Valued Optimal Control Problem
	14.3 Linear Discrete-Time Set-Valued Stackelberg Control Problem
	14.4 Linear Discrete-Time Set-Valued Pareto-Stackelberg Control Problem
	14.5 Linear Discrete-Time Set-Valued Nash-Stackelberg Control Problem
	14.6 Linear Discrete-Time Set-Valued Pareto-Nash-Stackelberg Control Problem
	14.7 Concluding Remarks
	References
15 Linear Discrete Pareto-Nash-Stackelberg Control Processes with Echoes & Retroactive Future
	15.1 Introduction
	15.2 Optimal Control of Linear Discrete-Time Processes with Periodic Echoes
	15.3 Optimal Control of Linear Discrete-Time Processes with Periodic Echoes and Retroactive Future
	15.4 Stackelberg Control of Linear Discrete-Time Processes with Periodic Echoes
	15.5 Stackelberg Control of Linear Discrete-Time Processes with Periodic Echoes and Retroactive  Future
	15.6 Pareto-Stackelberg Control of Discrete-Time Linear Processes with Periodic Echoes and Retroactive Future
	15.7 Nash-Stackelberg Control of Linear Discrete-Time Processes with Echoes and Retroactive Future
	15.8 Pareto-Nash-Stackelberg Control of Discrete-Time Linear Processes with Echoes and Retroactive Future
	15.9 Concluding Remarks
	References
Index