Skip to main content Accessibility help
×
Hostname: page-component-788cddb947-tr9hg Total loading time: 0 Render date: 2024-10-12T16:45:14.463Z Has data issue: false hasContentIssue false

10 - Introduction to Differential Games

Published online by Cambridge University Press:  05 October 2014

Pierre T. Kabamba
Affiliation:
University of Michigan, Ann Arbor
Anouck R. Girard
Affiliation:
University of Michigan, Ann Arbor
Get access

Summary

Game theory is an extension of control theory that deals with situations where several players exercise authority over a system. In general, each player may pursue its own objective. The players are not necessarily adversaries; they may choose to cooperate if it is to their advantage. In addition, the players may not know everything there is to know. They may act to learn what they do not know, or exploit the situation based on what they do know. This is a typical exploration-exploitation trade-off.

Game theory has applications to economics (several Nobel Prizes were awarded in this field), international diplomacy, guidance and pursuit evasion, warfare, and sports. Game theory is also applicable to control (see Figure 1.4), where the exogenous and endogenous inputs are two players in a game.

Section 10.1 presents a taxonomy of two-player games. Section 10.2 describes an example of a simple game of pursuit evasion in a two-player football scrimmage. Section 10.3 describes the Bellman-Isaacs equation. Sections 10.4 and 10.5 present modeling and features of the solution for the homicidal chauffeur game. Section 10.6 describes a game-theoretic view of proportional navigation. Sections 10.7, 10.8, and 10.9 present a summary of the key results in the chapter, bibliographic notes for further reading, and homework problems, respectively.

Taxonomy of Two-Player Games

We consider two-player games, in which the two players have control actions u and v, respectively.

Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2014

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×