The Adversarial Stackelberg Value in Quantitative Games
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 epsilon-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.
Keywords
Cite
@article{arxiv.2004.12918,
title = {The Adversarial Stackelberg Value in Quantitative Games},
author = {Emmanuel Filiot and Raffaella Gentilini and Jean-François Raskin},
journal= {arXiv preprint arXiv:2004.12918},
year = {2020}
}
Comments
long version of an ICALP'20 paper