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The Equilibrium Existence Problem in Finite Network Congestion Games

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Internet and Network Economics (WINE 2006)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 4286))

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Abstract

An open problem is presented regarding the existence of pure strategy Nash equilibrium (PNE) in network congestion games with a finite number of non-identical players, in which the strategy set of each player is the collection of all paths in a given network that link the player’s origin and destination vertices, and congestion increases the costs of edges. A network congestion game in which the players differ only in their origin–destination pairs is a potential game, which implies that, regardless of the exact functional form of the cost functions, it has a PNE. A PNE does not necessarily exist if (i) the dependence of the cost of each edge on the number of users is player- as well as edge-specific or (ii) the (possibly, edge-specific) cost is the same for all players but it is a function (not of the number but) of the total weight of the players using the edge, with each player i having a different weight w i . In a parallel two-terminal network, in which the origin and the destination are the only vertices different edges have in common, a PNE always exists even if the players differ in either their cost functions or weights, but not in both. However, for general two-terminal networks this is not so. The problem is to characterize the class of all two-terminal network topologies for which the existence of a PNE is guaranteed even with player-specific costs, and the corresponding class for player-specific weights. Some progress in solving this problem is reported.

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Author information

Authors and Affiliations

  1. Department of Economics, Bar-Ilan University, Ramat Gan, 52900, Israel

    Igal Milchtaich

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  1. Igal Milchtaich
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Editor information

Editors and Affiliations

  1. Department of Computer Engineering and Informatics, University of Patras, 26500, Rio, Patras, Greece

    Paul Spirakis

  2. Department of Computer Science, University of Cyprus, CY-1678, Nicosia, Cyprus

    Marios Mavronicolas

  3. R.A. Computer Technology Institute, N. Kazantzakis Str., University Campus, 26500, Rio–Patra, Greece

    Spyros Kontogiannis

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© 2006 Springer-Verlag Berlin Heidelberg

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Milchtaich, I. (2006). The Equilibrium Existence Problem in Finite Network Congestion Games. In: Spirakis, P., Mavronicolas, M., Kontogiannis, S. (eds) Internet and Network Economics. WINE 2006. Lecture Notes in Computer Science, vol 4286. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11944874_9

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  • DOI: https://doi.org/10.1007/11944874_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-68138-0

  • Online ISBN: 978-3-540-68141-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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