On the Existence of Nash Equilibria in Strategic Search Games

  • Carme Àlvarez
  • Amalia Duch
  • Maria Serna
  • Dimitrios Thilikos
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7173)


We consider a general multi-agent framework in which a set of n agents are roaming a network where m valuable and sharable goods (resources, services, information ….) are hidden in m different vertices of the network. We analyze several strategic situations that arise in this setting by means of game theory. To do so, we introduce a class of strategic games that we call strategic search games. In those games agents have to select a simple path in the network that starts from a predetermined set of initial vertices. Depending on how the value of the retrieved goods is splitted among the agents, we consider two game types: finders-share in which the agents that find a good split among them the corresponding benefit and firsts-share in which only the agents that first find a good share the corresponding benefit. We show that finders-share games always have pure Nash equilibria (pne ). For obtaining this result, we introduce the notion of Nash-preserving reduction between strategic games. We show that finders-share games are Nash-reducible to single-source network congestion games. This is done through a series of Nash-preserving reductions. For firsts-share games we show the existence of games with and without pne. Furthermore, we identify some graph families in which the firsts-share game has always a pne that is computable in polynomial time.


Nash Equilibrium Polynomial Time Polynomial Time Algorithm Directed Network Simple Path 
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  1. 1.
    Fabrikant, A., Papadimitriou, C., Talwar, K.: The complexity of pure Nash equilibria. In: Proceedings of the Thirty-Sixth Annual ACM Symposium on Theory of Computing (STOC), pp. 604–612 (2004)Google Scholar
  2. 2.
    Fotakis, D., Kontogiannis, S., Spirakis, P.: Symmetry in Network Congestion Games: Pure Equilibria and Anarchy Cost. In: Erlebach, T., Persinao, G. (eds.) WAOA 2005. LNCS, vol. 3879, pp. 161–175. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  3. 3.
    Gal, S.: Search Games. Academic Press (1980)Google Scholar
  4. 4.
    Isaacs, R.: Differential Games. John Wiley and Sons (1965)Google Scholar
  5. 5.
    Kontogiannis, S., Spirakis, P.: Atomic Selfish Routing in Networks: A Survey. In: Deng, X., Ye, Y. (eds.) WINE 2005. LNCS, vol. 3828, pp. 989–1002. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  6. 6.
    Koutsoupias, E., Papadimitriou, C.: Worst-Case Equilibria. In: Meinel, C., Tison, S. (eds.) STACS 1999. LNCS, vol. 1563, pp. 404–413. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  7. 7.
    Milchtaich, I.: Congestion games with player-specific payoff functions. Games and Economic Behavior 13(1), 111–124 (1996)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Nisan, N., Roughgarden, T., Tardos, E., Vazirani, V. (eds.): Algorithmic Game Theory. Cambridge University Press, New York (2007)zbMATHGoogle Scholar
  9. 9.
    Panagopoulou, P.N., Spirakis, P.G.: Efficient Convergence to Pure Nash Equilibria in Weighted Network Congestion Games. In: Nikoletseas, S.E. (ed.) WEA 2005. LNCS, vol. 3503, pp. 203–215. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  10. 10.
    Papadimitriou, C.: Algorithms, games, and the internet. In: STOC 2001: Proceedings of the Thirty-Third Annual ACM Symposium on Theory of Computing, pp. 749–753. ACM Press, New York (2001)CrossRefGoogle Scholar
  11. 11.
    Rosenthal, R.W.: A class of games possessing pure-strategy Nash equilibria. International Journal of Game Theory (2), 65–67 (1973)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Carme Àlvarez
    • 1
  • Amalia Duch
    • 1
  • Maria Serna
    • 1
  • Dimitrios Thilikos
    • 2
  1. 1.ALBCOM Research GroupTechnical University of CataloniaSpain
  2. 2.Department of MathematicsNational and Kapodistrian University of AthensGreece

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