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Optimally deceiving a learning leader in Stackelberg games

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Birmpas, Georgios, Gan, Jiarui, Hollender, Alexandros, Marmolejo-Cossío, Francisco J., Rajgopal, Ninad and Voudouris, Alexandros A. (2021) Optimally deceiving a learning leader in Stackelberg games. Journal of Artificial Intelligence Research, 72 . pp. 507-531. doi:10.1613/jair.1.12542 ISSN 1076-9757.

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Official URL: http://dx.doi.org/10.1613/jair.1.12542

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Abstract

Recent results have shown that algorithms for learning the optimal commitment in a Stackelberg game are susceptible to manipulation by the follower. These learning algorithms operate by querying the best responses of the follower, who consequently can deceive the algorithm by using fake best responses, typically by responding according to fake payoffs that are different from the actual ones. For this strategic behavior to be successful, the main challenge faced by the follower is to pinpoint the fake payoffs that would make the learning algorithm output a commitment that benefits them the most. While this problem has been considered before, the related literature has only focused on a simple setting where the follower can only choose from a finite set of payoff matrices, thus leaving the general version of the problem unanswered. In this paper, we fill this gap by showing that it is always possible for the follower to efficiently compute (near-)optimal fake payoffs, for various scenarios of learning interaction between the leader and the follower. Our results also establish an interesting connection between the follower’s deception and the leader’s maximin utility: through deception, the follower can induce almost any (fake) Stackelberg equilibrium if and only if the leader obtains at least their maximin utility in this equilibrium.

Item Type: Journal Article
Subjects: H Social Sciences > HB Economic Theory
Q Science > Q Science (General)
Q Science > QA Mathematics
Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software
Divisions: Faculty of Science, Engineering and Medicine > Science > Computer Science
Library of Congress Subject Headings (LCSH): Neural networks (Computer science) , Game theory, Game theory -- Mathematical models, Noncooperative games (Mathematics), Equilibrium (Economics), Machine learning , Mathematical optimization
Journal or Publication Title: Journal of Artificial Intelligence Research
Publisher: A A A I Press
ISSN: 1076-9757
Official Date: 27 October 2021
Dates:
DateEvent
27 October 2021Published
Volume: 72
Page Range: pp. 507-531
DOI: 10.1613/jair.1.12542
Status: Peer Reviewed
Publication Status: Published
Reuse Statement (publisher, data, author rights): ©2021 AI Access Foundation. All rights reserved https://jair.org/index.php/jair/about#jair-license
Access rights to Published version: Open Access (Creative Commons)
Date of first compliant deposit: 7 December 2021
Date of first compliant Open Access: 8 December 2021
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
639945 (ACCORD)European Research Councilhttp://dx.doi.org/10.13039/501100000781
788893 (AMDROMA)European Research Councilhttp://dx.doi.org/10.13039/501100000781
EP/N509711/1 [EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
945719[ERC] Horizon 2020 Framework Programmehttp://dx.doi.org/10.13039/100010661
1892947[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
MR/S031545/1UK Research and Innovationhttp://dx.doi.org/10.13039/100014013

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