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The Adversarial Stackelberg Value in Quantitative Games

Authors Emmanuel Filiot, Raffaella Gentilini, Jean-François Raskin

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ACM Subject Classification
  • Theory of computation → Solution concepts in game theory
  • Theory of computation → Logic and verification
Keywords
  • Non-zero sum games
  • reactive synthesis
  • adversarial Stackelberg

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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.

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Emmanuel Filiot, Raffaella Gentilini, and Jean-François Raskin. The Adversarial Stackelberg Value in Quantitative Games. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 127:1-127:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.ICALP.2020.127

Author Details

Emmanuel Filiot
  • Université libre de Bruxelles (ULB), Belgium
Raffaella Gentilini
  • University of Perugia, Italy
Jean-François Raskin
  • Université libre de Bruxelles (ULB), Belgium

Funding

This work is partially supported by the PDR project Subgame perfection in graph games (F.R.S.-FNRS), the MIS project F451019F (F.R.S.-FNRS), the ARC project Non-Zero Sum Game Graphs: Applications to Reactive Synthesis and Beyond (Fédération Wallonie-Bruxelles), the EOS project Verifying Learning Artificial Intelligence Systems (F.R.S.-FNRS & FWO), and the COST Action 16228 GAMENET (European Cooperation in Science and Technology). Emmanuel Filiot is associate researcher at F.R.S.-FNRS.

Acknowledgements

We thank anonymous reviewers, Dr. Shibashis Guha and Ms. Mrudula Balachander for useful comments on a preliminary version of this paper.

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