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The path player game

A network game from the point of view of the network providers

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Abstract

We introduce the path player game, a noncooperative network game with a continuum of mutually dependent set of strategies. This game models network flows from the point of view of competing network operators. The players are represented by paths in the network. They have to decide how much flow shall be routed along their paths. The competitive nature of the game is due to the following two aspects: First, a capacity bound on the overall network flow links the decisions of the players. Second, edges may be shared by several players which might have conflicting goals. In this paper, we prove the existence of feasible and pure-strategy equilibria in path player games, which is a nontrivial task due to noncontinuity of payoff functions and the infinite, mutually dependent strategy sets. We analyze different instances of path player games in more detail and present characterizations of equilibria for these cases.

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Authors and Affiliations

  1. Faculty of Mathematics, University of Sevilla, C/ Tarfia, s/n, 41012, Sevilla, Spain

    Justo Puerto

  2. Institute of Numerical and Applied Mathematics, University of Göttingen, Lotzestr. 16–18, 37083, Göttingen, Germany

    Anita Schöbel & Silvia Schwarze

Authors
  1. Justo Puerto
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  2. Anita Schöbel
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  3. Silvia Schwarze
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Correspondence to Silvia Schwarze.

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Puerto, J., Schöbel, A. & Schwarze, S. The path player game. Math Meth Oper Res 68, 1–20 (2008). https://doi.org/10.1007/s00186-007-0188-3

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  • DOI: https://doi.org/10.1007/s00186-007-0188-3

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