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)

Abstract

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.

Keywords

Nash Equilibrium Polynomial Time Polynomial Time Algorithm Directed Network Simple Path 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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