Advances in Dynamic Games and Their Applications: Analytical and Numerical Developments

Martino Bardi (auth.), Odile Pourtallier, Vladimir Gaitsgory, Pierre Bernhard (eds.)081764833X, 9780817648336

This book—an outgrowth of the 12th 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 progressing to applications of dynamic games in economics, finance, and energy supply.

Thematically organized into eight parts, the book covers key topics in these main areas:

* theoretical developments in general dynamic and differential games

* pursuit-evasion games

* numerical approaches to dynamic and differential games

* applications of dynamic games in economics and option pricing

* search games

* evolutionary games

* stopping games

* stochastic games and “large neighborhood” games

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.

Table of contents :
Front Matter….Pages 1-11
Front Matter….Pages 1-1
On Differential Games with Long-Time-Average Cost….Pages 1-16
Fields of Extremals and Sufficient Conditions for a Class of Variational Games….Pages 1-18
Linear Quadratic Differential Games: An Overview….Pages 1-34
A Neumann Boundary Control for Multidimensional Parabolic “Minmax” Control Problems….Pages 1-13
Non-Cooperative and Semi-Cooperative Differential Games….Pages 1-20
Front Matter….Pages 1-1
Some Geometrical Properties of the Phase Space Structure in Games on Manifolds….Pages 1-13
Strategies for Alternative Pursuit Games….Pages 1-11
Some Sufficient Conditions for Multi-Player Pursuit-Evasion Games with Continuous and Discrete Observations….Pages 1-13
Front Matter….Pages 1-1
A Numerical Approach to the ‘Princess and Monster’ Game on an Interval….Pages 1-9
Numerical Approximation and Optimal Strategies for Differential Games with Lack of Information on One Side….Pages 1-18
Fully-Discrete Schemes for the Value Function of Pursuit-Evasion Games with State Constraints….Pages 1-30
Numerical Solution of the Game of Two Cars with a Neurosimulator and Grid Computing….Pages 1-24
Numerical Investigation of the Value Function for the Homicidal Chauffeur Problem with a More Agile Pursuer….Pages 1-28
Front Matter….Pages 1-1
Credible Linear-Incentive Equilibrium Strategies in Linear-Quadratic Differential Games….Pages 1-31
Robust Control Approach to Digital Option Pricing:Synthesis Approach….Pages 1-18
Front Matter….Pages 1-1
A Search Game with a Strategy of Energy Supply for Target….Pages 1-25
The LQG Game Against Nature….Pages 1-15
Front Matter….Pages 1-1
Is Deterrence Evolutionarily Stable?….Pages 1-19
Evolutionarily Robust Strategies: Two Nontrivial Examples and a Theorem….Pages 1-19
Front Matter….Pages 1-1
Nash Equilibrium in a Game Version of the Elfving Problem…..Pages 1-16
Front Matter….Pages 1-1
Cooperative Strategies in Stopping Games….Pages 1-16
Front Matter….Pages 1-1
Pure Equilibrium Strategies for Stochastic Games via Potential Functions….Pages 1-12
Fibonacci Numbers and Equilibria in Large “Neighborhood” Games….Pages 1-18