The Adversarial Stackelberg Value in Quantitative Games

Authors Emmanuel Filiot, Raffaella Gentilini, Jean-François Raskin

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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


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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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)


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.

Subject Classification

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


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