Synthesis of controllable Nash equilibria in quantitative objective games

Shaull Almagor, Orna Kupferman, Giuseppe Perelli*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

13 Scopus citations


In Rational Synthesis, we consider a multi-agent system in which some of the agents are controllable and some are not. All agents have objectives, and the goal is to synthesize strategies for the controllable agents so that their objectives are satisfied, assuming rationality of the uncontrollable agents. Previous work on rational synthesis considers objectives in LTL, namely ones that describe on-going behaviors, and in Objective-LTL, which allows ranking of LTL formulas. In this paper, we extend rational synthesis to LTL[F]- an extension of LTL by quality operators. The satisfaction value of an LTL[F] formula is a real value in [0, 1], where the higher the value is, the higher is the quality in which the computation satisfies the specification. The extension significantly strengthens the framework of rational synthesis and enables a study its game- and social-choice theoretic aspects. In particular, we study the price of stability and price of anarchy of the rational-synthesis game and use them to explain the cooperative and non-cooperative settings of rational synthesis. Our algorithms make use of strategy logic and decision procedures for it. Thus, we are able to handle the richer quantitative setting using existing tools. In particular, we show that the cooperative and non-cooperative versions of quantitative rational synthesis are 2EXPTIME-complete and in 3EXP-TIME, respectively - not harder than the complexity known for their Boolean analogues.

Original languageAmerican English
Title of host publicationProceedings of the 27th International Joint Conference on Artificial Intelligence, IJCAI 2018
EditorsJerome Lang
PublisherInternational Joint Conferences on Artificial Intelligence
Number of pages7
ISBN (Electronic)9780999241127
StatePublished - 2018
Event27th International Joint Conference on Artificial Intelligence, IJCAI 2018 - Stockholm, Sweden
Duration: 13 Jul 201819 Jul 2018

Publication series

NameIJCAI International Joint Conference on Artificial Intelligence
ISSN (Print)1045-0823


Conference27th International Joint Conference on Artificial Intelligence, IJCAI 2018

Bibliographical note

Publisher Copyright:
© 2018 International Joint Conferences on Artificial Intelligence. All right reserved.


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