License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSTTCS.2014.351
URN: urn:nbn:de:0030-drops-48550
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2014/4855/
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Bouyer, Patricia ; Markey, Nicolas ; Stan, Daniel

Mixed Nash Equilibria in Concurrent Terminal-Reward Games

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Abstract

We study mixed-strategy Nash equilibria in multiplayer deterministic concurrent games played on graphs, with terminal-reward payoffs (that is, absorbing states with a value for each player). We show undecidability of the existence of a constrained Nash equilibrium (the constraint requiring that one player should have maximal payoff), with only three players and 0/1-rewards (i.e., reachability objectives). This has to be compared with the undecidability result by Ummels and Wojtczak for turn-based games which requires 14 players and general rewards. Our proof has various interesting consequences: (i) the undecidability of the existence of a Nash equilibrium with a constraint on the social welfare; (ii) the undecidability of the existence of an (unconstrained) Nash equilibrium in concurrent games with terminal-reward payoffs.

BibTeX - Entry

@InProceedings{bouyer_et_al:LIPIcs:2014:4855,
  author =	{Patricia Bouyer and Nicolas Markey and Daniel Stan},
  title =	{{Mixed Nash Equilibria in Concurrent Terminal-Reward Games}},
  booktitle =	{34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014)},
  pages =	{351--363},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-77-4},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{29},
  editor =	{Venkatesh Raman and S. P. Suresh},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2014/4855},
  URN =		{urn:nbn:de:0030-drops-48550},
  doi =		{10.4230/LIPIcs.FSTTCS.2014.351},
  annote =	{Keywords: concurrent games, randomized strategy, Nash equilibria, undecidability}
}

Keywords: concurrent games, randomized strategy, Nash equilibria, undecidability
Collection: 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014)
Issue Date: 2014
Date of publication: 12.12.2014

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