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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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N-Player Games

N-Player Games

Chapter:
(p.127) Lecture 11 N-Player Games
Source:
Noncooperative Game Theory
Author(s):

João P. Hespanha

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691175218.003.0011

This chapter extends several of the concepts for two-player games to games with N-players. It begins by considering general games with N players P₁, P₂, . . ., P(subscript N), which are allowed to select policies within action spaces Γ‎₁, Γ‎₂, . . ., Γ‎(subscript N). Each player wants to minimize their own outcome, and does not care about the outcome of the other players. The chapter proceeds by discussing the security level, security policy, and Nash equilibrium for N-player games, pure N-player games in normal form, mixed policy for N-player games in normal form, and computation of the completely mixed Nash equilibrium for N-player games. A mixed Nash equilibrium is computed for a different game in which some (or all) players want to maximize instead of minimize the outcome.

Keywords:   security level, security policy, Nash equilibrium, N-player game, pure N-player game, mixed policy, completely mixed Nash equilibrium

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