{"type":"ScholarlyArticle","title":"ATL Strategic Reasoning Meets Correlated Equilibrium","authors":[{"name":"Xiaowei Huang","slug":"xiaowei-huang","given":"Xiaowei","family":"Huang","affiliation":"School of Computing and Digital Technology , Birmingham City University , United Kingdom"},{"name":"Ji Ruan","slug":"ji-ruan","given":"Ji","family":"Ruan","affiliation":"Department of Computer Science , Auckland University of Technology , New Zealand"}],"abstract":"This paper is motivated by analysing a Google self-driving car accident, i.e., the car hit a bus,  with the framework and the tools of strategic reasoning by model checking. First of all, we find that existing ATL model checking may find a solution to the accident with {\\it irrational} joint strategy of the bus and the car. This leads to a restriction of treating both the bus and the car as rational agents, by which their joint strategy is an equilibrium of certain solution concepts. \r\nSecond, we find that a randomly-selected joint strategy from the set of equilibria may result in the collision of the two agents, i.e., the accident. \r\nBased on these, we suggest taking Correlated Equilibrium (CE) as agents' joint stratgey and optimising over the utilitarian value which is the expected sum of the agents' total rewards. The language ATL is extended with two new modalities to express the existence of an CE and a unique CE, respectively. \r\nWe implement the extension into a software model checker and use the tool to analyse the examples in the paper. We also study the complexity of the model checking problems.","doi":"10.24963/ijcai.2017/153","url":"https://ijcai.org/proceedings/2017/153","pdf":"https://ijcai.org/proceedings/2017/0153.pdf","markdown":"https://ijcai.org/proceedings/2017/153.md","bibtex":"https://ijcai.org/proceedings/2017/bibtex/153","volume":{"slug":"2017","title":"Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2017","url":"https://ijcai.org/proceedings/2017/","year":2017,"location":"Melbourne, Australia","dates":"19-25 August 2017","editors":"Carles Sierra, IIIA-CSIC","isbn":"978-0-9992411-0-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2017"},"section":"Knowledge Representation, Reasoning, and Logic","track":"Main track","number":153,"pages":{"first":1102,"last":1108},"keywords":["Agent-based and Multi-agent Systems: Coordination and cooperation","Knowledge Representation, Reasoning, and Logic: Automated Reasoning and Theorem Proving","Agent-based and Multi-agent Systems: Formal verification, validation and synthesis"],"videos":[],"references":[{"position":1,"raw":"[Alur and Henzinger, 1996] R. Alur and T.A. Henzinger. Re- active modules. In LICS1996, pages 207-218, 1996.","title":"Reactive modules","authors":"R Alur, T A Henzinger","year":"1996","venue":"LICS1996","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Alur et al., 1998] Rajeev Alur, Thomas A. Henzinger, F.Y.C. Mang, Shaz Qadeer, Sriram K. Rajamani, and Ser- dar Tasiran. Mocha: Modularity in model checking. In CAV 1998, pages 521-525, 1998.","title":"Mocha: Modularity in model checking","authors":"Rajeev Alur, Thomas A Henzinger, F Y C Mang, Shaz Qadeer, K Sriram, Serdar Rajamani, Tasiran","year":"1998","venue":"CAV 1998","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Alur et al., 2002] Rajeev Alur, Thomas A. Henzinger, and Orna Kupferman. Alternating-Time Temporal Logic. JACM, 49(5):672-713, 2002.","title":"Alternating-Time Temporal Logic","authors":"Rajeev Alur, Thomas A Henzinger, Orna Kupferman","year":"2002","venue":"JACM","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Aminof et al., 2016] Benjamin Aminof, Vadim Malvone, Aniello Murano, and Sasha Rubin. Graded strategy logic: Reasoning about uniqueness of nash equilibria. In AA- MAS2016, pages 698-706, 2016.","title":"Graded strategy logic: Reasoning about uniqueness of nash equilibria","authors":"Benjamin Aminof, Vadim Malvone, Aniello Murano, Sasha Rubin","year":"2016","venue":"AA-MAS2016","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Anand, 1993] Paul Anand. Foundations of Rational Choice Under Risk. Oxford University Press, 1993.","title":"Foundations of Rational Choice Under Risk","authors":"Paul Anand","year":"1993","venue":null,"doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Aumann, 1974] Robert Aumann. Subjectivity and correla- tion in randomized strategies. Journal of Mathematical Economics, 1:67-96, 1974.","title":"Subjectivity and correlation in randomized strategies","authors":"Robert Aumann","year":"1974","venue":"Journal of Mathematical Economics","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Aumann, 1987] Robert J. Aumann. Correlated equilibrium as an expression of bayesian rationality. Econometrica, 55(1):1-18, 1987.","title":"Correlated equilibrium as an expression of bayesian rationality","authors":"Robert J Aumann","year":"1987","venue":"Econometrica","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Busoniu et al., 2008] Lucian Busoniu, Robert Babuska, and Bart De Schutter. A comprehensive survey of multiagent reinforcement learning. IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews, 38(2):156-172, 2008.","title":"A comprehensive survey of multiagent reinforcement learning","authors":"Lucian Busoniu, Robert Babuska, Bart De Schutter","year":"2008","venue":"IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Čermák et al., 2014] Petr Čermák, Alessio Lomuscio, Fabio Mogavero, and Aniello Murano. Mcmas-slk: A model checker for the verification of strategy logic specifications. In CAV2014, pages 525-532, 2014.","title":"Mcmas-slk: A model checker for the verification of strategy logic specifications","authors":"Čermák","year":"2014","venue":"CAV2014","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Chatterjee and Henzinger, 2011] Krishnendu Chatterjee and Thomas A. Henzinger. A survey of stochastic -regular games. Journal of Computer and System Sciences, 78(2):394-413, 2011.","title":"A survey of stochastic -regular games","authors":"Krishnendu Chatterjee, Thomas A Henzinger","year":"2011","venue":"Journal of Computer and System Sciences","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Chatterjee et al., 2010] Krishnendu Chatterjee, Thomas A. Henzinger, and Nir Piterman. Strategy logic. Information and Computation, 208(6):677-693, 2010.","title":"Strategy logic","authors":"Krishnendu Chatterjee, Thomas A Henzinger, Nir Piterman","year":"2010","venue":"Information and Computation","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Chen et al., 2013] Taolue Chen, Vojtech Forejt, Marta Z. Kwiatkowska, David Parker, and Aistis Simaitis. Auto- matic verification of competitive stochastic systems. For- mal Methods in System Design, 43(1):61-92, 2013.","title":"Automatic verification of competitive stochastic systems","authors":"Chen","year":"2013","venue":"Formal Methods in System Design","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Clarke et al., 1999] E. M. Clarke, O. Grumberg, and D. Peled. Model Checking. The MIT Press, 1999.","title":"Model Checking","authors":"E M Clarke, O Grumberg, D Peled","year":"1999","venue":null,"doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Daskalakis et al., 2009] Constantinos Daskalakis, Paul W. Goldberg, and Christos H. Papadimitriou. The complex- ity of computing a nash equilibrium. SIAM Journal on Computing, 39(1):195-259, 2009.","title":"The complexity of computing a nash equilibrium","authors":"Constantinos Daskalakis, Paul W Goldberg, Christos H Papadimitriou","year":"2009","venue":"SIAM Journal on Computing","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Gilboa and Zemel, 1989] Itzhak Gilboa and Eitan Zemel. Nash and correlated equilibria: Some complexity consid- erations. Games and Economic Behavior, 1:80-93, 1989.","title":"Nash and correlated equilibria: Some complexity considerations","authors":"Zemel Gilboa, Itzhak Gilboa, Eitan Zemel","year":"1989","venue":"Games and Economic Behavior","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Goo, 2016] Google car accident report, Feb 2016.","title":"Google car accident report","authors":"Goo","year":"2016","venue":null,"doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Greenwald and Hall, 2003] Amy Greenwald and Keith Hall. Correlated q-learning. In ICML 2003, pages 242- 249, 2003.","title":"Correlated q-learning","authors":"Hall ; Greenwald, Amy Greenwald, Keith Hall","year":"2003","venue":"ICML 2003","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Huang and Luo, 2013] Xiaowei Huang and Cheng Luo. A logic of probabilistic knowledge and strategy. In AAMAS 2013, pages 845-852, 2013.","title":"A logic of probabilistic knowledge and strategy","authors":"Xiaowei Huang, Cheng Luo","year":"2013","venue":"AAMAS 2013","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Huang and van der Meyden, 2014a] Xiaowei Huang and Ron van der Meyden. Symbolic model checking epistemic strategy logic. In AAAI 2014, pages 1426-1432, 2014.","title":"Symbolic model checking epistemic strategy logic","authors":"Van Huang, Xiaowei Der Meyden, Ron Huang, Van Der Meyden","year":"2014","venue":"AAAI 2014","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Huang and van der Meyden, 2014b] Xiaowei Huang and Ron van der Meyden. A temporal logic of strategic knowl- edge. In KR 2014, 2014.","title":"A temporal logic of strategic knowledge","authors":"Van Huang, Xiaowei Der Meyden, Ron Huang, Van Der Meyden","year":"2014","venue":null,"doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Huang et al., 2012] Xiaowei Huang, Kaile Su, and Chenyi Zhang. Probabilistic alternating-time temporal logic. In AAAI 2012, pages 765-771, 2012.","title":"Probabilistic alternating-time temporal logic","authors":"Xiaowei Huang, Kaile Su, Chenyi Zhang","year":"2012","venue":"AAAI 2012","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Huang, 2015] Xiaowei Huang. Bounded model checking of strategy ability with perfect recall. Artificial Intelligence, pages 182-200, 2015.","title":"Bounded model checking of strategy ability with perfect recall","authors":"Xiaowei Huang","year":"2015","venue":"Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Koller and Pfeffer, 1995] Daphne Koller and Avi Pfeffer. Generating and solving imperfect information games. In IJCAI1995, pages 1185-1193, 1995.","title":"Generating and solving imperfect information games","authors":"Pfeffer Koller, Daphne Koller, Avi Pfeffer","year":"1995","venue":"IJCAI1995","doi":null,"url":null,"internal_url":"/proceedings/1995/153"},{"position":24,"raw":"[Mogavero et al., 2014] Fabio Mogavero, Aniello Murano, and Giuseppe Perelli. Reasoning about strategies: On the model-checking problem. ACM transactions on Computa- tional Logic, 2014.","title":"Reasoning about strategies: On the model-checking problem","authors":"Fabio Mogavero, Aniello Murano, Giuseppe Perelli","year":"2014","venue":"ACM transactions on Computational Logic","doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Nash, 1950] John Nash. Equilibrium points in n-person games. Proceedings of the National Academy of Sciences, 36(1):48-49, 1950.","title":"Equilibrium points in n-person games","authors":"John Nash","year":"1950","venue":"Proceedings of the National Academy of Sciences","doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[Sandholm, 2007] Tuomas Sandholm. Perspectives on mul- tiagent learning. Artifical Intelligence, 171:382-391, 2007.","title":"Perspectives on multiagent learning","authors":"Tuomas Sandholm, Sandholm","year":"2007","venue":"Artifical Intelligence","doi":null,"url":null,"internal_url":null},{"position":27,"raw":"[Shoham et al., 2007] Yoav Shoham, Rob Powers, and Trond Grenager. If multi-agent learning is the answer, what is the question? Artifical Intelligence, 171(7):365- 377, 2007.","title":"If multi-agent learning is the answer, what is the question?","authors":"Yoav Shoham, Rob Powers, Trond Grenager","year":"2007","venue":"Artifical Intelligence","doi":null,"url":null,"internal_url":null},{"position":28,"raw":"[Solan and Vieille, 2002] Eilon Solan and Nicolas Vieille. Correlated equilibrium in stochastic games. Games and Economic Behavior, pages 362-399, 2002.","title":"Correlated equilibrium in stochastic games","authors":"Vieille Solan, Eilon Solan, Nicolas Vieille","year":"2002","venue":"Games and Economic Behavior","doi":null,"url":null,"internal_url":null},{"position":29,"raw":"[TheVerge, 2016] TheVerge. A google self-driving car caused a crash for the first time -a bad assumption led to a minor fender-bender, 2016.","title":"TheVerge. A google self-driving car caused a crash for the first time -a bad assumption led to a minor fender-bender","authors":"Theverge","year":"2016","venue":null,"doi":null,"url":null,"internal_url":null},{"position":30,"raw":"[Toumi et al., 2015] Alexis Toumi, Julian Gutierrez, and Michael Wooldridge. A tool for the automated verification of nash equilibria in concurrent games. In ICTAC 2015, pages 583-594, 2015.","title":"A tool for the automated verification of nash equilibria in concurrent games","authors":"Alexis Toumi, Julian Gutierrez, Michael Wooldridge","year":"2015","venue":"ICTAC 2015","doi":null,"url":null,"internal_url":null},{"position":31,"raw":"[van der Hoek et al., 2005] Wiebe van der Hoek, Wojciech Jamroga, and Michael Wooldridge. A logic for strategic reasoning. In AAMAS 2005, pages 157-164, 2005.","title":"A logic for strategic reasoning","authors":"Hoek Van Der","year":"2005","venue":"AAMAS 2005","doi":null,"url":null,"internal_url":null},{"position":32,"raw":"[Wooldridge et al., 2016] Michael Wooldridge, Julian Gutierrez, Paul Harrenstein, Enrico Marchioni, Giuseppe Perelli, and Alexis Toumi. Rational verification: From model checking to equilibrium checking. In AAAI 2016, pages 4184-4191, 2016.","title":"Rational verification: From model checking to equilibrium checking","authors":"Michael Wooldridge, Julian Gutierrez, Paul Harrenstein, Enrico Marchioni, Giuseppe Perelli, Alexis Toumi","year":"2016","venue":"AAAI 2016","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}