Advances in Dynamic Games and Their Applications (eBook)

Analytical and Numerical Developments

Pierre Bernhard, Vladimir Gaitsgory, Odile Pourtallier (Herausgeber)

eBook Download: PDF

2009 | 2009
XIV, 462 Seiten
Birkhäuser Boston (Verlag)
978-0-8176-4834-3 (ISBN)

Infos

This book presents current advances in the theory of dynamic games and their applications in several disciplines. The selected contributions cover a variety of topics ranging from purely theoretical developments in game theory, to numerical analysis of various dynamic games, and then progressing to applications of dynamic games in economics, finance, and energy supply.

A unified collection of state-of-the-art advances in theoretical and numerical analysis of dynamic games and their applications, the work is suitable for researchers, practitioners, and graduate students in applied mathematics, engineering, economics, as well as environmental and management sciences.

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This book presents current advances in the theory of dynamic games and their applications in several disciplines. The selected contributions cover a variety of topics ranging from purely theoretical developments in game theory, to numerical analysis of various dynamic games, and then progressing to applications of dynamic games in economics, finance, and energy supply. Thematically organized into eight parts, the book covers key topics in these main areas: theoretical developments in general dynamic and differential games, pursuit-evasion games, numerical approaches to dynamic and differential games, applications of dynamic games in economics and option pricing, search games, evolutionary games, stopping games, and stochastic games and "e;large neighborhood"e; games.A unified collection of state-of-the-art advances in theoretical and numerical analysis of dynamic games and their applications, the work is suitable for researchers, practitioners, and graduate students in applied mathematics, engineering, economics, as well as environmental and management sciences.

Inhalt

Contents 6
Preface 9
Contributors 10
PART I Dynamic-Differential Games: Theoretical Developments 13
On Differential Games with Long-Time-Average Cost 14
Fields of Extremals and Sufficient Conditions for a Class of Variational Games 30
Linear Quadratic Differential Games: An Overview 48
A Neumann Boundary Control for Multidimensional Parabolic “ Minmax” Control Problems 82
Non-Cooperative and Semi-Cooperative Differential Games 95
PART II Pursuit- Evasion (P-E) Games 115
Some Geometrical Properties of the Phase Space Structure in Games on Manifolds 116
Strategies for Alternative Pursuit Games 129
Some Sufficient Conditions for Multi-Player Pursuit- Evasion Games with Continuous and Discrete Observations 140
PART III Numerical Approaches to Dynamic- Differential Games 153
A Numerical Approach to the ‘Princess and Monster’ Game on an Interval 154
Numerical Approximation and Optimal Strategies for Differential Games with Lack of Information on One Side 163
Fully-Discrete Schemes for the Value Function of Pursuit- Evasion Games with State Constraints 181
Numerical Solution of the Game of Two Cars with a Neurosimulator and Grid Computing 211
Numerical Investigation of the Value Function for the Homicidal Chauffeur Problem with a More Agile Pursuer 235
PART IV Applications 263
Credible Linear-Incentive Equilibrium Strategies in Linear- Quadratic Differential Games 264
Robust Control Approach to Digital Option Pricing: Synthesis Approach 295
PART V Search Games 313
A Search Game with a Strategy of Energy Supply for Target 314
The LQG Game Against Nature 339
PART VI Evolutionary Games 354
Is Deterrence Evolutionarily Stable? 355
Evolutionarily Robust Strategies: Two Nontrivial Examples and a Theorem 374
PART VII Stopping Games 393
Nash Equilibrium in a Game Version of the Elfving Problem 394
Cooperative Strategies in Stopping Games 410
PART VIII Stochastic Games and Large “ Neighborhood” Games 426
Pure Equilibrium Strategies for Stochastic Games via Potential Functions 427
Fibonacci Numbers and Equilibria in Large “ Neighborhood” Games 439

Produkt-Details

• Erscheint lt. Verlag: 20.4.2009
• Reihe/Serie: Annals of the International Society of Dynamic Games
• Reihe/Serie: Annals of the International Society of Dynamic Games
• Zusatzinfo: XIV, 462 p. 94 illus., 9 illus. in color.
• Verlagsort: Boston
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Finanz- / Wirtschaftsmathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Technik
• Themenwelt: Wirtschaft ► Allgemeines / Lexika
• Themenwelt: Wirtschaft ► Volkswirtschaftslehre
• Schlagworte: Applied mathematics • average • Calculus • Dynamic-Differential Games • Evolutionary Games • Function • Game Theory • "large neighborhood" games • linear optimization • manifold • Mathematics • Numerical analysis • Option pricing • pursuit-evasion games • Search Games • stochastic games • Theorem
• ISBN-10: 0-8176-4834-8 / 0817648348
• ISBN-13: 978-0-8176-4834-3 / 9780817648343