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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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PRINTED FROM PRINCETON SCHOLARSHIP ONLINE (www.princeton.universitypressscholarship.com). (c) Copyright Princeton University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in PRSO for personal use.date: 17 September 2021

Potential Games

Potential Games

(p.133) Lecture 12 Potential Games
Noncooperative Game Theory

João P. Hespanha

Princeton University Press

This chapter introduces a special class of N-player games, the so-called potential games, for which the Nash equilibrium is guaranteed to exist and is generally easy to find. It begins by considering a game with N players P₁, P₂, . . ., P(subscript N), which are allowed to select policies from the action spaces Γ‎₁, Γ‎₂, . . ., Γ‎(subscript N), respectively. The notation is given for the outcome of the game for the player Pᵢ and all players wanting to minimize their own outcomes. The chapter goes on to discuss identical interests games, minimum vs. Nash equilibrium in potential games, bimatrix potential games, characterization of potential games, and potential games with interval action spaces. It concludes with practice exercises and their corresponding solutions, along with an additional exercise.

Keywords:   potential game, Nash equilibrium, action space, identical interests, minimum, bimatrix potential

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