A geometric approach to the price of anarchy in nonatomic congestion games |
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Authors: | Jos R. Correa, Andreas S. Schulz,Nicol s E. Stier-Moses |
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Affiliation: | aSchool of Business, Universidad Adolfo Ibáñez, Av. Presidente Errázuriz 3485, Las Condes, Santiago, Chile;bSloan School of Management, Massachusetts Institute of Technology, Office E53-361, 77 Massachusetts Avenue, Cambridge, MA 02139, USA;cGraduate School of Business, Columbia University, Uris Hall, Room 418, 3022 Broadway Avenue, New York, NY 10027, USA |
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Abstract: | We present a short, geometric proof for the price-of-anarchy results that have recently been established in a series of papers on selfish routing in multicommodity flow networks and on nonatomic congestion games. This novel proof also facilitates two new types of theoretical results: On the one hand, we give pseudo-approximation results that depend on the class of allowable cost functions. On the other hand, we derive stronger bounds on the inefficiency of equilibria for situations in which the equilibrium costs are within reasonable limits of the fixed costs. These tighter bounds help to explain empirical observations in vehicular traffic networks. Our analysis holds in the more general context of nonatomic congestion games, which provide the framework in which we describe this work. |
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Keywords: | Noncooperative games Nonatomic games Congestion games Wardrop equilibrium Price of anarchy |
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