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International Conference on Foundations of Software Science and Computational Structures

FoSSaCS 2012: Foundations of Software Science and Computational Structures pp 286–300Cite as

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Subgame Perfection for Equilibria in Quantitative Reachability Games

Subgame Perfection for Equilibria in Quantitative Reachability Games

  • Thomas Brihaye17,
  • Véronique Bruyère17,
  • Julie De Pril17 &
  • …
  • Hugo Gimbert18 
  • Conference paper
  • 885 Accesses

  • 2 Citations

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7213)

Abstract

We study turn-based quantitative multiplayer non zero-sum games played on finite graphs with reachability objectives. In such games, each player aims at reaching his own goal set of states as soon as possible. A previous work on this model showed that Nash equilibria (resp. secure equilibria) are guaranteed to exist in the multiplayer (resp. two-player) case. The existence of secure equilibria in the multiplayer case remained, and is still an open problem. In this paper, we focus our study on the concept of subgame perfect equilibrium, a refinement of Nash equilibrium well-suited in the framework of games played on graphs. We also introduce the new concept of subgame perfect secure equilibrium. We prove the existence of subgame perfect equilibria (resp. subgame perfect secure equilibria) in multiplayer (resp. two-player) quantitative reachability games. Moreover, we provide an algorithm deciding the existence of secure equilibria in the multiplayer case.

Keywords

  • Nash Equilibrium
  • Subgame Perfect Equilibrium
  • Initial Vertex
  • Subgame Perfection
  • Quantitative Objective

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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Author information

Authors and Affiliations

  1. University of Mons - UMONS, Place du Parc 20, 7000, Mons, Belgium

    Thomas Brihaye, Véronique Bruyère & Julie De Pril

  2. LaBRI & CNRS, Bordeaux, France

    Hugo Gimbert

Authors
  1. Thomas Brihaye
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  2. Véronique Bruyère
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  3. Julie De Pril
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  4. Hugo Gimbert
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Editor information

Editors and Affiliations

  1. IT University of Copenhagen, Rued Langgaards Vej 7, 2300, Copenhagen, Denmark

    Lars Birkedal

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Brihaye, T., Bruyère, V., De Pril, J., Gimbert, H. (2012). Subgame Perfection for Equilibria in Quantitative Reachability Games. In: Birkedal, L. (eds) Foundations of Software Science and Computational Structures. FoSSaCS 2012. Lecture Notes in Computer Science, vol 7213. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28729-9_19

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