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Differential Games: A Concise Introduction

Houston Powell

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Differential Games: A Concise Introduction

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Language	:	English
File size	:	30976 KB
Text-to-Speech	:	Enabled
Screen Reader	:	Supported
Enhanced typesetting	:	Enabled
Print length	:	336 pages

Differential games are a class of dynamic games in which the players' decisions influence the evolution of a continuous state variable. Differential games are used to model a wide variety of applications, including pursuit-evasion games, economic competition, and environmental management.

Basic Concepts

A differential game is typically defined by the following elements:

A set of players
A state space
A set of actions for each player
A dynamics function that describes how the state of the game evolves over time
An objective function for each player

The players in a differential game make decisions sequentially. At each decision point, each player chooses an action that maximizes their objective function, given the current state of the game and the actions of the other players.

Solution Methods

There are a variety of methods for solving differential games. Some of the most common methods include:

The method of characteristics
The Hamilton-Jacobi-Bellman equation
The Pontryagin maximum principle

The method of characteristics is a geometric method that can be used to solve differential games in which the dynamics function is linear.

The Hamilton-Jacobi-Bellman equation is a partial differential equation that can be used to solve differential games in which the dynamics function is nonlinear.

The Pontryagin maximum principle is a variational principle that can be used to solve differential games in which the dynamics function is nonlinear and the objective functions are linear.

Applications

Differential games have a wide range of applications, including:

Pursuit-evasion games
Economic competition
Environmental management
Resource allocation
Robotics

In pursuit-evasion games, differential games can be used to model the behavior of pursuers and evaders. In economic competition, differential games can be used to model the behavior of competing firms. In environmental management, differential games can be used to model the behavior of polluters and regulators.

Differential games are a powerful tool for modeling and analyzing dynamic systems. Differential games have a wide range of applications, including pursuit-evasion games, economic competition, and environmental management. The basic concepts of differential games are relatively simple, but the solution methods can be complex. However, there are a number of resources available to help you learn more about differential games.

References

Basar, T., & Bernhard, P. (1995). Differential games and applications. Berlin: Springer.
Isaacs, R. (1965). Differential games. New York: John Wiley & Sons.
Petrosjan, L. A., & Zenkevich, N. A. (1996). Game theory. Berlin

Differential Games: A Concise Introduction

5 out of 5