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.ICALP.2020.127
URN: urn:nbn:de:0030-drops-125348
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12534/
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Filiot, Emmanuel ; Gentilini, Raffaella ; Raskin, Jean-François

The Adversarial Stackelberg Value in Quantitative Games

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LIPIcs-ICALP-2020-127.pdf (0.6 MB)

Abstract

In this paper, we study the notion of adversarial Stackelberg value for two-player non-zero sum games played on bi-weighted graphs with the mean-payoff and the discounted sum functions. The adversarial Stackelberg value of Player 0 is the largest value that Player 0 can obtain when announcing her strategy to Player 1 which in turn responds with any of his best response. For the mean-payoff function, we show that the adversarial Stackelberg value is not always achievable but ε-optimal strategies exist. We show how to compute this value and prove that the associated threshold problem is in NP. For the discounted sum payoff function, we draw a link with the target discounted sum problem which explains why the problem is difficult to solve for this payoff function. We also provide solutions to related gap problems.

BibTeX - Entry

@InProceedings{filiot_et_al:LIPIcs:2020:12534,
  author =	{Emmanuel Filiot and Raffaella Gentilini and Jean-Fran{\c{c}}ois Raskin},
  title =	{{The Adversarial Stackelberg Value in Quantitative Games}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{127:1--127:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Artur Czumaj and Anuj Dawar and Emanuela Merelli},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12534},
  URN =		{urn:nbn:de:0030-drops-125348},
  doi =		{10.4230/LIPIcs.ICALP.2020.127},
  annote =	{Keywords: Non-zero sum games, reactive synthesis, adversarial Stackelberg}
}

Keywords: Non-zero sum games, reactive synthesis, adversarial Stackelberg
Collection: 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)
Issue Date: 2020
Date of publication: 29.06.2020

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