Fasoulakis, Michail (2017) Computing approximate Nash equilibria. PhD thesis, University of Warwick.

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Abstract

The problem of finding equilibria in non-cooperative games and understanding their properties is a central problem in modern game theory. After John Nash proved that every finite game has at least one equilibrium (so-called Nash equilibrium), the natural question arose whether we can compute one efficiently. After several years of extensive research, we now know that the problem of finding a Nash equilibrium is PPAD-complete even for two-player normal-form games, making the task of finding approximate Nash equilibria one of the central questions in the area of equilibrium computation. In this thesis our main goal is a new study of the complexity of various variants of the approximate Nash equilibrium. Specifically, we study algorithms for additive approximate Nash equilibria in bimatrix and multi-player games. Then, we study algorithms for relative approximate Nash equilibria in multi-player games. Furthermore, we study algorithms for optimal approximate Nash equilibria in bimatrix games and finally we study the communication complexity of additive approximate Nash equilibria in bimatrix games.

Item Type:	Thesis or Dissertation (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Game theory, Noncooperative games (Mathematics), Equilibrium (Economics), Algorithms
Official Date:	2017
Dates:	Date Event 2017 Submitted
Institution:	University of Warwick
Theses Department:	Department of Computer Science
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Czumaj, Artur ; Jurdziński, Marcin
Format of File:	pdf
Extent:	vii, 133 leaves : illustrations
Language:	eng

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