Bouyer, Patricia ;
Markey, Nicolas ;
Stan, Daniel
Mixed Nash Equilibria in Concurrent Terminal-Reward Games
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}
}
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Keywords: |
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concurrent games, randomized strategy, Nash equilibria, undecidability |
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Seminar: |
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34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014)
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Issue date: |
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2014 |
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Date of publication: |
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2014 |
2014
