Advances in Dynamic Games

by Breton, Michele; Szajowski, Krzysztof

• ISBN13: 9780817680886
• ISBN10: 0817680888
• Format: Hardcover
• Copyright: 2010-12-01
• Publisher: Birkhauser

Summary

This self-contained book'”an outgrowth of the 13th International Symposium on Dynamic Games'”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 progresses to applications of dynamic games to communication and transportation networks, economics, finance, management science, environmental science, biology, and social science.The book covers key topics in these main areas:* dynamic games and applications* repeated games* stochastic games* learning and adaptive games* mechanism design* evolutionary games* cooperative equilibria* h-infinity control and robust controller designs* theory of optimal control and dynamic games* numerical methods and computer implementation of game-theoretic models* dynamic bargaining* pursuit-evasion games* Dynkin's game and its application* search, encounter, and inspection gamesA 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 the environmental, life, social, and management sciences.

Table of Contents

Foreword	p. vii
Preface	p. xiii
Acknowledgements	p. xv
A Tribute to Arik Artavazdovich Melikyan	p. xvii
Testimonies	p. xix
Arik A. Melikyan (10.05.1944-04.06.2009)	p. xxv
Bibliography of Works	p. xxix
The Long History of Arik's Conjecture	p. xxxvii
Optimal Control Problem for a Dynamical System on an Ellipsoid	p. xxxix
Contributors	p. xliii
Dynamic-Differential Games: Theoretical Developments
On a Structure of the Set of Differential Games Values	p. 3
Existence and Uniqueness of Disturbed Open-Loop Nash Equilibria for Affine-Quadratic Differential Games	p. 25
Fields of Extremals and Sufficient Conditions for a Class of Open-Loop Variational Games	p. 41
Riemann-Liouville, Caputo, and Sequential Fractional Derivatives in Differential Games	p. 61
The Mixed Zero-Sum Stochastic Differential Game in the Model with Jumps	p. 83
Discontinuous Value Function in Time-Optimal Differential Games	p. 111
On Grid Optimal Feedbacks to Control Problems of Prescribed Duration on the Plane	p. 133
Sub- and Super-optimality Principles and Construction of Almost Optimal Strategies for Differential Games in Hilbert Spaces	p. 149
Pursuit Evasion Games
Extremal Aiming in Problems with Unknown Level of Dynamic Disturbance	p. 167
A Generalization of the Multi-Stage Search Allocation Game	p. 189
Linear Differential Game with Two Pursuers and One Evader	p. 209
Homicidal Chauffeur Game: History and Modern Studies	p. 227
Collision Avoidance Strategies for a Three-Player Game	p. 253
Evolutionary Games
Imitative Behavior in a Two-Population Model	p. 275
ESS, Population Games, Replicator Dynamics: Dynamics and Games if not Dynamic Games	p. 291
A Markov Decision Evolutionary Game for Individual Energy Management	p. 313
Mutual Mate Choice with Multiple Criteria	p. 337
Cooperative Games
The Shapley Value in Cooperative Differential Games with Random Duration	p. 359
Dynamically Consistent Cooperative Solutions in Differential Games with Asynchronous Players' Horizons	p. 375
Applications and Numerical Approaches
Measure-Valued Solutions to a Harvesting Game with Several Players	p. 399
Optimal Distributed Uplink Channel Allocation: A Constrained MDP Formulation	p. 425
Binomial Approximations for Barrier Options of Israeli Style	p. 447
A Game of International Climate Policy Solved by a Homogeneous Oracle-Based Method for Variational Inequalities	p. 469
Optimal Stopping of a Risk Process with Disruption and Interest Rates	p. 489
Examples in Dynamic Optimal Taxation	p. 509
On a Discounted Inventory Game	p. 521
Time-Consistent Emission Reduction in a Dynamic Leader-Follower Game	p. 537
Fish Wars with Changing Area for a Fishery	p. 553
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