Author: Dianyu Jiang
Language: English
ISBN/ISSN: 1933100340
Published on: 2010-01
Hardcover
In this book, the author introduces Shannon entropy and principle of maximum entropy into n-person strategic games whose every of players has exactly 2 pure strategies. Principle of minimum entropy is put forth. Some 0-1 numbering and criterions symmetry and duality of the games are given. The method to find pure Nash equilibria and completely mixed Nash equilibria are obtained. Method to solve expected equilibria and corresponding equilibrium analysis based on principle of maximum entropy are researched. Marginal-able correlated equilibria and optimal situation analysis are focused on 2-person and 3-person games.
The readers of this book can be undergraduates, Master’s degree students, doctoral students, university teacher and researchers and so forth with the study fields applied mathematics, operations research, game theory, economics, management scienec and engineering, systems science and systems engineering, information and control, etc.
Preface
Chapter 0 Introduction
Chapter 1 Entropy of Discrete Random Variables
1.1 Uncertainty and Entropy of Discrete Random Variables
1.2 Properties of Entropy
1.3 Principles of Maximum and Minimum Entropies
Chapter 2 Symmetry and 0-1 Number of an N-Person Double
Action Game
2.1 An N-Person 0-1 Games, Symmetry and Duality
2.2 Explicit Symmetry, Implicit Symmetry and Non-Symmetry
2.3 The First Discriminating and 0-1 Numbering Methods for
Implicit and Non- Symmetrical Games
2.4 The Second Discriminating and 0-1 Numbering Methods for
Implicit and Non- Symmetrical Games
Chapter 3 Strictly Pure Nash Equilibria and Expected Equilibrium
Analysis of N-Person 0-1 Games
3.1 N-M Stable Set and Strictly Pure Nash Equilibria n an N-Person 0-1
Game and its Dual
3.2 An Algorithm of Strictly Pure Nash Equilibria in an N-Person 0-1
Game
3.3 Formulas to Compute Expected Equilibria
3.4 Examples of Computing Expected Equilibria and Strictly Pure Nash
Equilibria
3.5 Some Examples about Analysis of Expected Equilibrium
Chapter 4 Completely Mixed Nash Equilibria for 0-1 Games
4.1 Basic Concepts
4.2 Pascal Derived Matrices
4.3 Finding CMNE in a Symmetrical 0-1 Game and its Inverse
Question
4.4 Some Theorems on 3-Person 0-1 Games
Chapter 5 Situation Analysis of 2-Person 0-1 Games
5.1 Existence of CMNE
5.2 Discriminating Vectors
5.3 Set of Marginal-able Correlated Equilibria on a CMNE
5.4 Entropy Function on a Set of Marginal-able Correlated Equilibria
5.5 Optimal Situation Analysis
5.6 PN-Games
5.9 Relation Between an Optimal Situation an Expected
Equilibria
Chapter 6 Situation Analysis of 3-Person 0-1 Games
6.1 Some Pre-Results on N (N≥3)-Person 0-1 Games
6.2 Set of Marginal-able Correlated Equilibria and Optimal Situation
Distribution for a Game Form (0,△S(1), △S(2))
6.3 Set of Marginal-able Correlated Equilibria and Optimal Situation
Distribution for a Game Form (△S(0),0,△S(2))
6.4 Set of Marginal-able Correlated Equilibria and Optimal Situation
Distribution for a Game Form (△S(0),△S(1),0)
6.5 Set of Marginal-able Correlated Equilibria and Optimal Situation
Distribution for a Game Form (△S(0),△S(0),△S(2))
6.6 Set of Marginal-able Correlated Equilibria and Optimal Situation
Distribution for a Game Form (△S(0),△S(1),△S(0))
6.7 Set of Marginal-able Correlated Equilibria and Optimal Situation
Distribution for a Game Form (△S(0),△S(1),△S(1))
6.8 Set of Marginal-able Correlated Equilibria and Optimal Situation
Distribution for a Game Form (△S(0),△S(1),△S(2))
6.9 Some Examples of Set of Marginal-able Correlated Equilibria and
Optimal Situation Distribution for a Game Form (△S(0),△S(0),△(2))
6.10 Discussion about Sets of Marginal-able Correlated Equilibria in
2- and N (N≥3) -Person 0-1 Games
6.11 Summary of this Chapter
Chapter 7 Some Examples of Situation Analysis of 2-Person 0-1
Games
7.1 Battle of the Sexes
7.2 Hawk – Dove Games
7.3 Game of Chicken
7.4 Game of Doing Good Things
7.5 Game of Warriors
7.6 Game Between Two Clever Pigs
7.7 Poor - Rich Patrolling Game
Chapter 8 Some Examples of Situation Analysis of 3-Person 0-1
Games
8.1 Game of Three Business Alliance and Game of Digging Ginseng
8.2 Pirates Game and Guards’ Best Defense Force
8.3 Confession Game
8.4 Game Among Three People of Digging Herbs
8.5 Public Goods Game
8.6 Game Among Three Pirates
8.7 Group Game
References
Index
Language: English
ISBN/ISSN: 1933100340
Published on: 2010-01
Hardcover
In this book, the author introduces Shannon entropy and principle of maximum entropy into n-person strategic games whose every of players has exactly 2 pure strategies. Principle of minimum entropy is put forth. Some 0-1 numbering and criterions symmetry and duality of the games are given. The method to find pure Nash equilibria and completely mixed Nash equilibria are obtained. Method to solve expected equilibria and corresponding equilibrium analysis based on principle of maximum entropy are researched. Marginal-able correlated equilibria and optimal situation analysis are focused on 2-person and 3-person games.
The readers of this book can be undergraduates, Master’s degree students, doctoral students, university teacher and researchers and so forth with the study fields applied mathematics, operations research, game theory, economics, management scienec and engineering, systems science and systems engineering, information and control, etc.
Preface
Chapter 0 Introduction
Chapter 1 Entropy of Discrete Random Variables
1.1 Uncertainty and Entropy of Discrete Random Variables
1.2 Properties of Entropy
1.3 Principles of Maximum and Minimum Entropies
Chapter 2 Symmetry and 0-1 Number of an N-Person Double
Action Game
2.1 An N-Person 0-1 Games, Symmetry and Duality
2.2 Explicit Symmetry, Implicit Symmetry and Non-Symmetry
2.3 The First Discriminating and 0-1 Numbering Methods for
Implicit and Non- Symmetrical Games
2.4 The Second Discriminating and 0-1 Numbering Methods for
Implicit and Non- Symmetrical Games
Chapter 3 Strictly Pure Nash Equilibria and Expected Equilibrium
Analysis of N-Person 0-1 Games
3.1 N-M Stable Set and Strictly Pure Nash Equilibria n an N-Person 0-1
Game and its Dual
3.2 An Algorithm of Strictly Pure Nash Equilibria in an N-Person 0-1
Game
3.3 Formulas to Compute Expected Equilibria
3.4 Examples of Computing Expected Equilibria and Strictly Pure Nash
Equilibria
3.5 Some Examples about Analysis of Expected Equilibrium
Chapter 4 Completely Mixed Nash Equilibria for 0-1 Games
4.1 Basic Concepts
4.2 Pascal Derived Matrices
4.3 Finding CMNE in a Symmetrical 0-1 Game and its Inverse
Question
4.4 Some Theorems on 3-Person 0-1 Games
Chapter 5 Situation Analysis of 2-Person 0-1 Games
5.1 Existence of CMNE
5.2 Discriminating Vectors
5.3 Set of Marginal-able Correlated Equilibria on a CMNE
5.4 Entropy Function on a Set of Marginal-able Correlated Equilibria
5.5 Optimal Situation Analysis
5.6 PN-Games
5.9 Relation Between an Optimal Situation an Expected
Equilibria
Chapter 6 Situation Analysis of 3-Person 0-1 Games
6.1 Some Pre-Results on N (N≥3)-Person 0-1 Games
6.2 Set of Marginal-able Correlated Equilibria and Optimal Situation
Distribution for a Game Form (0,△S(1), △S(2))
6.3 Set of Marginal-able Correlated Equilibria and Optimal Situation
Distribution for a Game Form (△S(0),0,△S(2))
6.4 Set of Marginal-able Correlated Equilibria and Optimal Situation
Distribution for a Game Form (△S(0),△S(1),0)
6.5 Set of Marginal-able Correlated Equilibria and Optimal Situation
Distribution for a Game Form (△S(0),△S(0),△S(2))
6.6 Set of Marginal-able Correlated Equilibria and Optimal Situation
Distribution for a Game Form (△S(0),△S(1),△S(0))
6.7 Set of Marginal-able Correlated Equilibria and Optimal Situation
Distribution for a Game Form (△S(0),△S(1),△S(1))
6.8 Set of Marginal-able Correlated Equilibria and Optimal Situation
Distribution for a Game Form (△S(0),△S(1),△S(2))
6.9 Some Examples of Set of Marginal-able Correlated Equilibria and
Optimal Situation Distribution for a Game Form (△S(0),△S(0),△(2))
6.10 Discussion about Sets of Marginal-able Correlated Equilibria in
2- and N (N≥3) -Person 0-1 Games
6.11 Summary of this Chapter
Chapter 7 Some Examples of Situation Analysis of 2-Person 0-1
Games
7.1 Battle of the Sexes
7.2 Hawk – Dove Games
7.3 Game of Chicken
7.4 Game of Doing Good Things
7.5 Game of Warriors
7.6 Game Between Two Clever Pigs
7.7 Poor - Rich Patrolling Game
Chapter 8 Some Examples of Situation Analysis of 3-Person 0-1
Games
8.1 Game of Three Business Alliance and Game of Digging Ginseng
8.2 Pirates Game and Guards’ Best Defense Force
8.3 Confession Game
8.4 Game Among Three People of Digging Herbs
8.5 Public Goods Game
8.6 Game Among Three Pirates
8.7 Group Game
References
Index
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