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Noncooperative Game TheoryAn Introduction for Engineers and Computer Scientists$
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João P. Hespanha

Print publication date: 2017

Print ISBN-13: 9780691175218

Published to Princeton Scholarship Online: May 2018

DOI: 10.23943/princeton/9780691175218.001.0001

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Games in Extensive Form

Games in Extensive Form

Chapter:
(p.71) Lecture 7 Games in Extensive Form
Source:
Noncooperative Game Theory
Author(s):

João P. Hespanha

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691175218.003.0007

This chapter discusses a number of key concepts for extensive form game representation. It first considers a matrix that defines a zero-sum matrix game for which the minimizer has two actions and the maximizer has three actions and shows that the matrix description, by itself, does not capture the information structure of the game and, in fact, other information structures are possible. It then describes an extensive form representation of a zero-sum two-person game, which is a decision tree, the extensive form representation of multi-stage games, and the notions of security policy, security level, and saddle-point equilibrium for a game in extensive form. It also explores the matrix form for games in extensive form, recursive computation of equilibria for single-stage games, feedback games, feedback saddle-point for multi-stage games, and recursive computation of equilibria for multi-stage games. It concludes with a practice exercise with the corresponding solution, along with additional exercises.

Keywords:   extensive form game representation, zero-sum matrix, zero-sum two-person, multi-stage game, security policy, security level, saddle-point equilibrium, single-stage game, feedback game, recursive computation

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