Advances in Dynamic Games (eBook)

Foreword 7
Contents 8
Preface 12
Acknowledgements 14
A Tribute to Arik Artavazdovich Melikyan 15
Testimonies 16
Arik A. Melikyan ( 10.05.1944– 04.06.2009) 22
Bibliography of Works by Arik A. Melikyan 25
The Long History of Arik’s Conjecture 33
Optimal Control Problem for a Dynamical System on an Ellipsoid 35
Contributors 39
Dynamic-Differential Games: Theoretical Developments 43
On a Structure of the Set of Differential Games Values 44
Existence and Uniqueness of Disturbed Open- Loop Nash Equilibria for Affine- Quadratic Differential Games 65
Fields of Extremals and Sufficient Conditions for a Class of Open- Loop Variational Games 80
Riemann–Liouville, Caputo, and Sequential Fractional Derivatives in Differential Games 99
The Mixed Zero-Sum Stochastic Differential Game in the Model with Jumps 120
Discontinuous Value Function in Time-Optimal Differential Games 148
On Grid Optimal Feedbacks to Control Problems of Prescribed Duration on the Plane 169
Sub- and Super-optimality Principles and Construction of Almost Optimal Strategies for Differential Games in Hilbert Spaces 184
Pursuit Evasion Games 199
Extremal Aiming in Problems with Unknown Level of Dynamic Disturbance 200
A Generalization of the Multi-Stage Search Allocation Game 221
Linear Differential Game with Two Pursuers and One Evader 240
Homicidal Chauffeur Game: History and Modern Studies 258
Collision Avoidance Strategies for a Three- Player Game 283
Evolutionary Games 302
Imitative Behavior in a Two-Population Model 303
ESS, Population Games, Replicator Dynamics: Dynamics and Games if not Dynamic Games 318
A Markov Decision Evolutionary Game for Individual Energy Management 339
Mutual Mate Choice with Multiple Criteria 362
Cooperative Games 381
The Shapley Value in Cooperative Differential Games with Random Duration 382
Dynamically Consistent Cooperative Solutions in Differential Games with Asynchronous Players’ Horizons 397
Applications and Numerical Approaches 418
Measure-Valued Solutions to a Harvesting Game with Several Players 419
Optimal Distributed Uplink Channel Allocation: A Constrained MDP Formulation 444
Binomial Approximations for Barrier Options of Israeli Style 465
A Game of International Climate Policy Solved by a Homogeneous Oracle- Based Method for Variational Inequalities 486
Optimal Stopping of a Risk Process with Disruption and Interest Rates 506
Examples in Dynamic Optimal Taxation 525
On a Discounted Inventory Game 537
Time-Consistent Emission Reduction in a Dynamic Leader- Follower Game 553
Fish Wars with Changing Area for a Fishery 569