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DOI: 10.4230/LIPIcs.CONCUR.2019.13
URN: urn:nbn:de:0030-drops-109153
URL: http://drops.dagstuhl.de/opus/volltexte/2019/10915/
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Brihaye, Thomas ; Bruyère, Véronique ; Goeminne, Aline ; Raskin, Jean-François ; van den Bogaard, Marie

The Complexity of Subgame Perfect Equilibria in Quantitative Reachability Games

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LIPIcs-CONCUR-2019-13.pdf (0.5 MB)


Abstract

We study multiplayer quantitative reachability games played on a finite directed graph, where the objective of each player is to reach his target set of vertices as quickly as possible. Instead of the well-known notion of Nash equilibrium (NE), we focus on the notion of subgame perfect equilibrium (SPE), a refinement of NE well-suited in the framework of games played on graphs. It is known that there always exists an SPE in quantitative reachability games and that the constrained existence problem is decidable. We here prove that this problem is PSPACE-complete. To obtain this result, we propose a new algorithm that iteratively builds a set of constraints characterizing the set of SPE outcomes in quantitative reachability games. This set of constraints is obtained by iterating an operator that reinforces the constraints up to obtaining a fixpoint. With this fixpoint, the set of SPE outcomes can be represented by a finite graph of size at most exponential. A careful inspection of the computation allows us to establish PSPACE membership.

BibTeX - Entry

@InProceedings{brihaye_et_al:LIPIcs:2019:10915,
  author =	{Thomas Brihaye and V{\'e}ronique Bruy{\`e}re and Aline Goeminne and Jean-Fran{\c{c}}ois Raskin and Marie van den Bogaard},
  title =	{{The Complexity of Subgame Perfect Equilibria in Quantitative Reachability Games}},
  booktitle =	{30th International Conference on Concurrency Theory (CONCUR 2019)},
  pages =	{13:1--13:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-121-4},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{140},
  editor =	{Wan Fokkink and Rob van Glabbeek},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/10915},
  URN =		{urn:nbn:de:0030-drops-109153},
  doi =		{10.4230/LIPIcs.CONCUR.2019.13},
  annote =	{Keywords: multiplayer non-zero-sum games played on graphs, quantitative reachability objectives, subgame perfect equilibria, constrained existence problem}
}

Keywords: multiplayer non-zero-sum games played on graphs, quantitative reachability objectives, subgame perfect equilibria, constrained existence problem
Seminar: 30th International Conference on Concurrency Theory (CONCUR 2019)
Issue Date: 2019
Date of publication: 26.08.2019


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