Bernhard / Pourtallier / Gaitsgory Advances in Dynamic Games and Their Applications

Analytical and Numerical Developments
1. Auflage 2009
ISBN: 978-0-8176-4834-3
Verlag: Birkhäuser Boston
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 10, 462 Seiten

Reihe: Annals of the International Society of Dynamic Games

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.

Autoren/Hrsg.

Pourtallier, Odile

Gaitsgory, Vladimir

Bernhard, Pierre

Inhaltsverzeichnis

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