{"type":"ScholarlyArticle","title":"Synthesis of Controllable Nash Equilibria in Quantitative Objective Game","authors":[{"name":"Shaull Almagor","slug":"shaull-almagor","given":"Shaull","family":"Almagor","affiliation":"University of Oxford"},{"name":"Orna Kupferman","slug":"orna-kupferman","given":"Orna","family":"Kupferman","affiliation":"Hebrew University"},{"name":"Giuseppe Perelli","slug":"giuseppe-perelli","given":"Giuseppe","family":"Perelli","affiliation":"University of Oxford"}],"abstract":"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 3EXPTIME, respectively -- not harder than the complexity known for their Boolean analogues.","doi":"10.24963/ijcai.2018/5","url":"https://ijcai.org/proceedings/2018/5","pdf":"https://ijcai.org/proceedings/2018/0005.pdf","markdown":"https://ijcai.org/proceedings/2018/5.md","bibtex":"https://ijcai.org/proceedings/2018/bibtex/5","volume":{"slug":"2018","title":"Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2018","url":"https://ijcai.org/proceedings/2018/","year":2018,"location":"Stockholm","dates":"13-19 July 2018","editors":"Jérôme Lang","isbn":"978-0-9992411-2-7","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2018"},"section":"Agent-based and Multi-agent Systems","track":"Main track","number":5,"pages":{"first":35,"last":41},"keywords":["Agent-based and Multi-agent Systems: Noncooperative Games","Agent-based and Multi-agent Systems: Formal Verification, Validation and Synthesis"],"videos":[],"references":[{"position":1,"raw":"[Almagor et al., 2015] S. Almagor, G. Avni, and O. Kupferman. Repairing Multi-Player Games. In CONCUR'15, pages 325-339, 2015.","title":"Repairing Multi-Player Games","authors":"S Almagor, G Avni, O Kupferman","year":"2015","venue":"CONCUR'15","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Almagor et al., 2016] S. Almagor, U. Boker, and O. Kupferman. Formalizing and reasoning about quality. J. ACM, 63(3), 2016.","title":"Formalizing and reasoning about quality","authors":"S Almagor, U Boker, O Kupferman","year":"2016","venue":"J. ACM","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Anshelevich et al., 2008] E. Anshelevich, A. Dasgupta, J. Klein- berg, E. Tardos, T. Wexler, and T. Roughgarden. The price of stability for network design with fair cost allocation. SIAM J. Comput., 38(4):1602-1623, 2008.","title":"The price of stability for network design with fair cost allocation","authors":"E Anshelevich, A Dasgupta, J Kleinberg, E Tardos, T Wexler, T Roughgarden","year":"2008","venue":"SIAM J. Comput","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Condurache et al., 2016] R. Condurache, E. Filiot, R. Gentilini, and J. Raskin. The complexity of rational synthesis. In Proc. ICALP'16, pages 121:1-121:15, 2016.","title":"The complexity of rational synthesis","authors":"R Condurache, E Filiot, R Gentilini, J Raskin","year":"2016","venue":"Proc. ICALP'16","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Faella et al., 2008] M. Faella, A. Legay, and M. Stoelinga. Model checking quantitative linear time logic. Electr. Notes Theor. Com- put. Sci., 220(3):61-77, 2008.","title":"Model checking quantitative linear time logic","authors":"M Faella, A Legay, M Stoelinga","year":"2008","venue":"Electr. Notes Theor. Comput. Sci","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Fisman et al., 2010] D. Fisman, O. Kupferman, and Y. Lustig. Ra- tional synthesis. In Proc. 16th TACAS, LNCS 6015, pages 190- 204, 2010.","title":"Rational synthesis","authors":"D Fisman, O Kupferman, Y Lustig","year":"2010","venue":"Proc. 16th TACAS","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Gutierrez et al., 2015] J. Gutierrez, P. Harrenstein, and M. Wooldridge. Iterated Boolean Games. Information and Computation, 242:53-79, 2015.","title":"Iterated Boolean Games","authors":"J Gutierrez, P Harrenstein, M Wooldridge","year":"2015","venue":"Information and Computation","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Gutierrez et al., 2016] J. Gutierrez, G. Perelli, and M. Wooldridge. Imperfect Information in Reactive Modules Games. In Proc. KR'16, pages 390-400, 2016.","title":"Imperfect Information in Reactive Modules Games","authors":"J Gutierrez, G Perelli, M Wooldridge","year":"2016","venue":"Proc. KR'16","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Gutierrez et al., 2017a] J. Gutierrez, A. Murano, G. Perelli, S. Ru- bin, and M. Wooldridge. Nash equilibria in concurrent games with lexicographic preferences. In Proc. IJCAI'17, pages 1067- 1073, 2017.","title":"Nash equilibria in concurrent games with lexicographic preferences","authors":"Gutierrez","year":"2017","venue":"Proc. IJCAI'17","doi":null,"url":null,"internal_url":"/proceedings/2017/148"},{"position":10,"raw":"[Gutierrez et al., 2017b] J. Gutierrez, G. Perelli, and M. Wooldridge. Iterated games with LDL goals over finite traces. In Proc. AAMAS'17, pages 696-704, 2017.","title":"Iterated games with LDL goals over finite traces","authors":"Gutierrez","year":"2017","venue":"Proc. AAMAS'17","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Gutierrez et al., 2018] J. Gutierrez, G. Perelli, and M. Wooldridge. Imperfect information in reactive modules games. Information and Computation, 2018. Article in Press.","title":"Imperfect information in reactive modules games","authors":"J Gutierrez, G Perelli, M Wooldridge","year":"2018","venue":"Information and Computation","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Harel and Pnueli, 1985] D. Harel and A. Pnueli. On the develop- ment of reactive systems. In Logics and Models of Concurrent Systems, pages 477-498. Springer, 1985.","title":"On the development of reactive systems","authors":"D Harel, A Pnueli","year":"1985","venue":"Logics and Models of Concurrent Systems","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Harrenstein et al., 2001] P. Harrenstein, W. van der Hoek, J. Meyer, and C. Witteveen. Boolean games. In Proc. 8th TARK, pages 287-298, 2001.","title":"Boolean games","authors":"P Harrenstein, W Van Der Hoek, J Meyer, C Witteveen","year":"2001","venue":"Proc. 8th TARK","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Koutsoupias and Papadimitriou, 2009] E. Koutsoupias and C. Pa- padimitriou. Worst-case equilibria. Computer Science Review, 3(2):65-69, 2009.","title":"Worst-case equilibria","authors":"E Koutsoupias, C","year":"2009","venue":"Computer Science Review","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Kupferman et al., 2016] O. Kupferman, G. Perelli, and M.Y. Vardi. Synthesis with rational environments. Ann. Math. Artif. Intell., 78(1):3-20, 2016.","title":"Synthesis with rational environments","authors":"O Kupferman, G Perelli, M Y Vardi","year":"2016","venue":"Ann. Math. Artif. Intell","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Mogavero et al., 2010] F. Mogavero, A. Murano, and M.Y. Vardi. Reasoning About Strategies. In Proc. 30th FSTTCS, LIPIcs 8, pages 133-144, 2010.","title":"Reasoning About Strategies","authors":"F Mogavero, A Murano, M Y Vardi","year":"2010","venue":"Proc. 30th FSTTCS, LIPIcs 8","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Mogavero et al., 2012] F. Mogavero, A. Murano, G. Perelli, and M.Y. Vardi. What Makes ATL* Decidable? A Decidable Frag- ment of Strategy Logic. In Proc. 23rd CONCUR, LNCS 7454, pages 193-208, 2012.","title":"What Makes ATL* Decidable? A Decidable Fragment of Strategy Logic","authors":"F Mogavero, A Murano, G Perelli, M Y Vardi","year":"2012","venue":"Proc. 23rd CONCUR","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Mogavero et al., 2014] F. Mogavero, A. Murano, G. Perelli, and M.Y. Vardi. Reasoning About Strategies: On the Model- Checking Problem. ACM Transactions on Computational Logic, 15(4):34:1-47, 2014.","title":"Reasoning About Strategies: On the Model-Checking Problem","authors":"F Mogavero, A Murano, G Perelli, M Y Vardi","year":"2014","venue":"ACM Transactions on Computational Logic","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Mogavero et al., 2017] F. Mogavero, A. Murano, G. Perelli, and M. Y. Vardi. Reasoning about strategies: on the satisfiability problem. Logical Methods in Computer Science, 13(1), 2017.","title":"Reasoning about strategies: on the satisfiability problem","authors":"F Mogavero, A Murano, G Perelli, M Y Vardi","year":"2017","venue":"Logical Methods in Computer Science","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Nash, 1950] J.F. Nash. Equilibrium points in n-person games. In Proceedings of the National Academy of Sciences of the United States of America, 1950.","title":"Equilibrium points in n-person games","authors":"J F Nash","year":"1950","venue":"Proceedings of the National Academy of Sciences of the United States of America","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Nisan and Ronen, 1999] N. Nisan and A. Ronen. Algorithmic mechanism design. In Proc. 31st STOC, pages 129-140, 1999.","title":"Algorithmic mechanism design","authors":"N Nisan, A Ronen","year":"1999","venue":"Proc. 31st STOC","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Nisan et al., 2007] N. Nisan, T. Roughgarden, E. Tardos, and V.V. Vazirani. Algorithmic Game Theory. Cambridge University Press, 2007.","title":"Algorithmic Game Theory","authors":"N Nisan, T Roughgarden, E Tardos, V V Vazirani","year":"2007","venue":null,"doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Papadimitriou, 2001] C. H. Papadimitriou. Algorithms, games, and the internet. In Proc. 33rd STOC, pages 749-753, 2001.","title":"Algorithms, games, and the internet","authors":"C H Papadimitriou","year":"2001","venue":"Proc. 33rd STOC","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Pnueli and Rosner, 1989] A. Pnueli and R. Rosner. On the synthe- sis of a reactive module. In Proc. 16th POPL, pages 179-190, 1989.","title":"On the synthesis of a reactive module","authors":"A Pnueli, R Rosner","year":"1989","venue":"Proc. 16th POPL","doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Wooldridge et al., 2016] M. Wooldridge, J. Gutierrez, P. Harren- stein, E. Marchioni, G. Perelli, and A. Toumi. Rational verifi- cation: From model checking to equilibrium checking. In Proc. AAAI'16, pages 4184-4191. AAAI Press, 2016.","title":"Rational verification: From model checking to equilibrium checking","authors":"M Wooldridge, J Gutierrez, P Harrenstein, E Marchioni, G Perelli, A Toumi","year":"2016","venue":"Proc. AAAI'16","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}