Advances in Dynamic Games and Their Applications (eBook)

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