Pub. Date:
Birkhäuser Boston
Advances in Dynamic Games: Theory, Applications, and Numerical Methods for Differential and Stochastic Games / Edition 1

Advances in Dynamic Games: Theory, Applications, and Numerical Methods for Differential and Stochastic Games / Edition 1


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This book focuses on various aspects of dynamic game theory, presenting state-of-the-art research and serving as a testament to the vitality and growth of the field of dynamic games and their applications. The selected contributions, written by experts in their respective disciplines, are outgrowths of presentations originally given at the 13th International Symposium of Dynamic Games and Applications held in Wrocław. The book covers a variety of topics, ranging from theoretical developments in game theory and algorithmic methods to applications, examples, and analysis in fields as varied as environmental management, finance and economics, engineering, guidance and control, and social interaction.

Product Details

ISBN-13: 9780817680886
Publisher: Birkhäuser Boston
Publication date: 12/01/2010
Series: Annals of the International Society of Dynamic Games , #11
Edition description: 2011
Pages: 565
Product dimensions: 6.10(w) x 9.25(h) x 0.24(d)

Table of Contents

Foreword vii

Preface xiii

Acknowledgements xv

A Tribute to Arik Artavazdovich Melikyan xvii

Testimonies xix

Arik A. Melikyan (10.05.1944-04.06.2009) xxv

Bibliography of Works Arik A. Melikyan xxix

The Long History of Arik's Conjecture Pierre Bernhard xxxvii

Optimal Control Problem for a Dynamical System on an Ellipsoid Arik A. Melikyan Fumiaki Imado xxxix

Contributors xliii

Part I Dynamic-Differential Games: Theoretical Developments

On a Structure of the Set of Differential Games Values Yurii Averboukh 3

Existence and Uniqueness of Disturbed Open-Loop Nash Equilibria for Affine-Quadratic Differential Games Teresa-Paula Azevedo-Perdicoúlis Gerhard Jank 25

Fields of Extremals and Sufficient Conditions for a Class of Open-Loop Variational Games Dean A. Carlson George Leitmann 41

Riemann-Liouville, Caputo, and Sequential Fractional Derivatives in Differential Games Arkadii Chikrii Ivan Matychyn 61

The Mixed Zero-Sum Stochastic Differential Game in the Model with Jumps Saïd Hamadène Hao Wang 83

Discontinuous Value Function in Time-Optimal Differential Games Liudmila Kamneva 111

On Grid Optimal Feedbacks to Control Problems of Prescribed Duration on the Plane Nina N. Subbotina Timofey B. Tokmantsev 133

Sub- and Super-optimality Principles and Construction of Almost Optimal Strategies for Differential Games in Hilbert Spaces Andrzej Swiech 149

Part II Pursuit Evasion Games

Extremal Aiming in Problems with Unknown Level of Dynamic Disturbance Sergei A. Ganebny Sergey S. Kumkov Valerii S. Patsko Sergei G. Pyatko 167

A Generalization of the Multi-Stage Search Allocation Game Ryusuke Hohzaki 189

Linear Differential Game with Two Pursuers and One Evader Stéphane Le Ménec 209

Homicidal Chauffeur Game: History and Modern Studies Valerii S. Patsko Varvara L. Turova 227

Collision Avoidance Strategies for a Three-Player Game Sriram Shankaran Dusan M. Stipanovic Claire J. Tomlin 253

Part III Evolutionary Games

Imitative Behavior in a Two-Population Model Elvio Accinelli Juan Gabriel Brida Edgar J. Sanchez Carrera 275

ESS, Population Games, Replicator Dynamics: Dynamics and Games if not Dynamic Games Pierre Bernhard 291

A Markov Decision Evolutionary Game for Individual Energy Management Yezekael Hayel Hamidou Tembine Eitan Altman Rachid El-Azouzi 313

Mutual Mate Choice with Multiple Criteria David M. Ramsey 337

Part IV Cooperative Games

The Shapley Value in Cooperative Differential Games with Random Duration Ekaterina Shevkoplyas 359

Dynamically Consistent Cooperative Solutions in Differential Games with Asynchronous Players' Horizons David W.K. Yeung 375

Part V Applications and Numerical Approaches

Measure-Valued Solutions to a Harvesting Game with Several Players Alberto Bressan Wen Shen 399

Optimal Distributed Uplink Channel Allocation: A Constrained MDP Formulation Vivek S. Borkar Joy Kuri 425

Binomial Approximations for Barrier Options of Israeli Style Yan Dolinsky Yuri Kifer 447

A Game of International Climate Policy Solved by a Homogeneous Oracle-Based Method for Variational Inequalities Laurent Drouet Alain Haurie Jean-Philippe Vial Marc Vielle 469

Optimal Stopping of a Risk Process with Disruption and Interest Rates Elzbieta Z. Ferenstein Adam Pasternak-Winiarski 489

Examples in Dynamic Optimal Taxation Mikhail Krastanov Rossen Rozenov 509

On a Discounted Inventory Game Heinz-Uwe Küenle 521

Time-Consistent Emission Reduction in a Dynamic Leader-Follower Game Yulia Pavlova 537

Fish Wars with Changing Area for a Fishery Anna Rettieva 553

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