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The path player game

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  • Justo Puerto
  • Anita Schöbel
  • Silvia Schwarze

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. Copyright Springer-Verlag 2008

Suggested Citation

  • Justo Puerto & Anita Schöbel & Silvia Schwarze, 2008. "The path player game," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 68(1), pages 1-20, August.
    • Handle: RePEc:spr:mathme:v:68:y:2008:i:1:p:1-20
    DOI: 10.1007/s00186-007-0188-3
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    References listed on IDEAS

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    1. Goh, C. J. & Yang, X. Q., 1999. "Vector equilibrium problem and vector optimization," European Journal of Operational Research, Elsevier, vol. 116(3), pages 615-628, August.
    2. Jackson, Matthew O., 2005. "Allocation rules for network games," Games and Economic Behavior, Elsevier, vol. 51(1), pages 128-154, April.
    3. Goyal, Sanjeev & Vega-Redondo, Fernando, 2005. "Network formation and social coordination," Games and Economic Behavior, Elsevier, vol. 50(2), pages 178-207, February.
    4. Gomez, Daniel & Gonzalez-Aranguena, Enrique & Manuel, Conrado & Owen, Guillermo & del Pozo, Monica & Tejada, Juan, 2003. "Centrality and power in social networks: a game theoretic approach," Mathematical Social Sciences, Elsevier, vol. 46(1), pages 27-54, August.
    5. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, December.
    6. Yann Bramoullé & Dunia López-Pintado & Sanjeev Goyal & Fernando Vega-Redondo, 2004. "Network formation and anti-coordination games," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(1), pages 1-19, January.
    7. José R. Correa & Andreas S. Schulz & Nicolás E. Stier-Moses, 2004. "Selfish Routing in Capacitated Networks," Mathematics of Operations Research, INFORMS, vol. 29(4), pages 961-976, November.
    8. Ramesh Johari & John N. Tsitsiklis, 2004. "Efficiency Loss in a Network Resource Allocation Game," Mathematics of Operations Research, INFORMS, vol. 29(3), pages 407-435, August.
    9. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
    10. Harker, Patrick T., 1991. "Generalized Nash games and quasi-variational inequalities," European Journal of Operational Research, Elsevier, vol. 54(1), pages 81-94, September.
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