{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,24]],"date-time":"2026-09-24T21:38:18Z","timestamp":1790285898212,"version":"4.1.0"},"reference-count":48,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2020,6,13]],"date-time":"2020-06-13T00:00:00Z","timestamp":1592006400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,6,13]],"date-time":"2020-06-13T00:00:00Z","timestamp":1592006400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100011199","name":"FP7 Ideas: European Research Council","doi-asserted-by":"publisher","award":["291528"],"award-info":[{"award-number":["291528"]}],"id":[{"id":"10.13039\/100011199","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Acta Informatica"],"published-print":{"date-parts":[[2021,12]]},"DOI":"10.1007\/s00236-020-00385-4","type":"journal-article","created":{"date-parts":[[2020,6,13]],"date-time":"2020-06-13T09:02:52Z","timestamp":1592038972000},"page":"585-610","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Equilibria for games with combined qualitative and quantitative objectives"],"prefix":"10.1007","volume":"58","author":[{"given":"Julian","family":"Gutierrez","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Aniello","family":"Murano","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8687-6323","authenticated-orcid":false,"given":"Giuseppe","family":"Perelli","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sasha","family":"Rubin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Thomas","family":"Steeples","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Michael","family":"Wooldridge","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2020,6,13]]},"reference":[{"key":"385_CR1","unstructured":"Alechina, N., Logan, B., Nga, N.H., Raimondi, F.: Model-checking for resource-bounded ATL with production and consumption of resources. CoRR, arXiv:1504.06766 (2015)"},{"key":"385_CR2","doi-asserted-by":"crossref","unstructured":"Almagor, S., Kupferman, O., Perelli, G.: Synthesis of controllable Nash equilibria in quantitative objective game. In: Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence, IJCAI 2018, July 13\u201319, 2018, Stockholm, Sweden, pp. 35\u201341 (2018)","DOI":"10.24963\/ijcai.2018\/5"},{"key":"385_CR3","volume-title":"Principles of Cyber-Physical Systems","author":"R Alur","year":"2015","unstructured":"Alur, R.: Principles of Cyber-Physical Systems. The MIT Press, Cambridge (2015)"},{"issue":"5","key":"385_CR4","doi-asserted-by":"publisher","first-page":"672","DOI":"10.1145\/585265.585270","volume":"49","author":"R Alur","year":"2002","unstructured":"Alur, R., Henzinger, T.A., Kupferman, O.: Alternating-time temporal logic. J. ACM 49(5), 672\u2013713 (2002)","journal-title":"J. ACM"},{"key":"385_CR5","volume-title":"Digraphs: Theory, Algorithms and Applications","author":"J Bang-Jensen","year":"2008","unstructured":"Bang-Jensen, J., Gutin, G.: Digraphs: Theory, Algorithms and Applications. Springer, Berlin (2008)"},{"key":"385_CR6","volume-title":"Fun and Games: A Text on Game Theory","author":"K Binmore","year":"1992","unstructured":"Binmore, K.: Fun and Games: A Text on Game Theory. D. C. Heath and Company, Lexington (1992)"},{"key":"385_CR7","doi-asserted-by":"crossref","unstructured":"Bloem, R., Chatterjee, K., Henzinger, T.A., Jobstmann, B.: Better quality in synthesis through quantitative objectives. In: CAV\u201909, pp. 140\u2013156 (2009)","DOI":"10.1007\/978-3-642-02658-4_14"},{"key":"385_CR8","unstructured":"Bonzon, E., Lagasquie, M.-C., Lang, J., Zanuttini, B.: Boolean games revisited. In: Proceedings of the Seventeenth European Conference on Artificial Intelligence (ECAI-2006), Riva del Garda, Italy (2006)"},{"key":"385_CR9","doi-asserted-by":"publisher","DOI":"10.2168\/LMCS-11(2:9)2015","author":"P Bouyer","year":"2015","unstructured":"Bouyer, P., Brenguier, R., Markey, N., Ummels, M.: Pure Nash equilibria in concurrent deterministic games. Log. Methods Comput. Sci. (2015). https:\/\/doi.org\/10.2168\/LMCS-11(2:9)2015","journal-title":"Log. Methods Comput. Sci."},{"key":"385_CR10","doi-asserted-by":"publisher","first-page":"52","DOI":"10.1016\/j.artint.2012.08.005","volume":"198","author":"R Brafman","year":"2013","unstructured":"Brafman, R., Domshlak, C.: On the complexity of planning for agent teams and its implications for single agent planning. Artif. Intell. 198, 52\u201371 (2013)","journal-title":"Artif. Intell."},{"key":"385_CR11","unstructured":"Brafman, R., Domshlak, C., Engel, Y., Tennenholtz, M.: Planning games. In: Proceedings of the Twenty-First International Joint Conference on Artificial Intelligence (IJCAI-09) (2009)"},{"key":"385_CR12","doi-asserted-by":"crossref","unstructured":"Bruy\u00e8re, V., Meunier, N., Raskin, J.-F.: Secure equilibria in weighted games. In: CSL-LICS\u201914, pp. 26:1\u201326:26 (2014)","DOI":"10.1145\/2603088.2603109"},{"key":"385_CR13","doi-asserted-by":"crossref","unstructured":"Bulling, N., Goranko, V.: How to be both rich and happy: combining quantitative and qualitative strategic reasoning about multi-player games (extended abstract). In: SR\u201913, pp. 33\u201341 (2013","DOI":"10.4204\/EPTCS.112.8"},{"key":"385_CR14","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1016\/j.tcs.2012.07.038","volume":"458","author":"K Chatterjee","year":"2012","unstructured":"Chatterjee, K., Doyen, L.: Energy parity games. Theor. Comput. Sci. 458, 49\u201360 (2012)","journal-title":"Theor. Comput. Sci."},{"key":"385_CR15","unstructured":"Chatterjee, K., Henzinger, T.A., Jurdzinski, M.: Mean-payoff parity games. In: LICS\u201905, pp. 178\u2013187 (2005)"},{"issue":"6","key":"385_CR16","doi-asserted-by":"publisher","first-page":"677","DOI":"10.1016\/j.ic.2009.07.004","volume":"208","author":"K Chatterjee","year":"2010","unstructured":"Chatterjee, K., Henzinger, T.A., Piterman, N.: Strategy logic. Inf. Comput. 208(6), 677\u2013693 (2010)","journal-title":"Inf. Comput."},{"key":"385_CR17","volume-title":"Model Checking","author":"EM Clarke","year":"2000","unstructured":"Clarke, E.M., Grumberg, O., Peled, D.A.: Model Checking. The MIT Press, Cambridge (2000)"},{"key":"385_CR18","volume-title":"Temporal Logics in Computer Science","author":"S Demri","year":"2017","unstructured":"Demri, S., Goranko, V., Lange, M.: Temporal Logics in Computer Science. Cambridge University Press, Cambridge (2017)"},{"key":"385_CR19","unstructured":"Dunne, P.E., Kraus, S., van der Hoek, W., Wooldridge, M.: Cooperative Boolean games. In: Proceedings of the Seventh International Joint Conference on Autonomous Agents and Multiagent Systems (AAMAS-2008), Estoril, Portugal (2008)"},{"issue":"2","key":"385_CR20","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1007\/BF01768705","volume":"8","author":"A Ehrenfeucht","year":"1979","unstructured":"Ehrenfeucht, A., Mycielski, J.: Positional strategies for mean payoff games. Int. J. Game Theory 8(2), 109\u2013113 (1979)","journal-title":"Int. J. Game Theory"},{"key":"385_CR21","first-page":"996","volume-title":"Handbook of Theoretical Computer Science Volume B: Formal Models and Semantics","author":"EA Emerson","year":"1990","unstructured":"Emerson, E.A.: Temporal and modal logic. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science Volume B: Formal Models and Semantics, pp. 996\u20131072. Elsevier, Amsterdam (1990)"},{"key":"385_CR22","doi-asserted-by":"crossref","unstructured":"Fisman, D., Kupferman, O., Lustig, Y.: Rational synthesis. In: TACAS\u201910, pp. 190\u2013204. Springer (2010)","DOI":"10.1007\/978-3-642-12002-2_16"},{"key":"385_CR23","unstructured":"Grant, J., Kraus, S., Wooldridge, M., Zuckerman, I.: Manipulating Boolean games through communication. In: Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence (IJCAI-11), Barcelona, Catalonia, Spain (2011)"},{"key":"385_CR24","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1016\/j.ic.2015.03.011","volume":"242","author":"J Gutierrez","year":"2015","unstructured":"Gutierrez, J., Harrenstein, P., Wooldridge, M.: Iterated Boolean games. Inf. Comput. 242, 53\u201379 (2015)","journal-title":"Inf. Comput."},{"key":"385_CR25","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1016\/j.artint.2017.04.003","volume":"248","author":"J Gutierrez","year":"2017","unstructured":"Gutierrez, J., Harrenstein, P., Wooldridge, M.: From model checking to equilibrium checking: reactive modules for rational verification. Artif. Intell. 248, 123\u2013157 (2017)","journal-title":"Artif. Intell."},{"key":"385_CR26","doi-asserted-by":"publisher","DOI":"10.23638\/LMCS-15(3:32)2019","author":"J Gutierrez","year":"2019","unstructured":"Gutierrez, J., Harrenstein, P., Perelli, G., Wooldridge, M.J.: Nash equilibrium and bisimulation invariance. Log. Methods Comput. Sci. (2019). https:\/\/doi.org\/10.23638\/LMCS-15(3:32)2019","journal-title":"Log. Methods Comput. Sci."},{"key":"385_CR27","doi-asserted-by":"crossref","unstructured":"Gutierrez, J., Murano, A., Perelli, G., Rubin, S., Wooldridge, M.J.: Nash equilibria in concurrent games with lexicographic preferences. In: IJCAI, pp. 1067\u20131073 (2017)","DOI":"10.24963\/ijcai.2017\/148"},{"key":"385_CR28","unstructured":"Harrenstein, P., van der Hoek, W., Meyer, J.-J.Ch., Witteveen, C.: Boolean games. In: van Benthem, J. (ed.) Proceeding of the Eighth Conference on Theoretical Aspects of Rationality and Knowledge (TARK VIII), Siena, Italy, pp. 287\u2013298 (2001)"},{"key":"385_CR29","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.artint.2018.04.006","volume":"261","author":"E Ianovski","year":"2018","unstructured":"Ianovski, E., Ong, L.: The complexity of decision problems about equilibria in two-player Boolean games. Artif. Intell. 261, 1\u201315 (2018)","journal-title":"Artif. Intell."},{"issue":"3","key":"385_CR30","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1016\/S0020-0190(98)00150-1","volume":"68","author":"M Jurdzinski","year":"1998","unstructured":"Jurdzinski, M.: Deciding the winner in parity games is in UP $$\\cap $$ co-UP. Inf. Process. Lett. 68(3), 119\u2013124 (1998)","journal-title":"Inf. Process. Lett."},{"key":"385_CR31","doi-asserted-by":"crossref","unstructured":"Kosaraju, S.R., Sullivan, G.: Detecting cycles in dynamic graphs in polynomial time. In: STOC\u201988, pp. 398\u2013406. ACM (1988)","DOI":"10.1145\/62212.62251"},{"issue":"1","key":"385_CR32","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/s10472-016-9508-8","volume":"78","author":"O Kupferman","year":"2016","unstructured":"Kupferman, O., Perelli, G., Vardi, M.Y.: Synthesis with rational environments. Ann. Math. Artif. Intell. 78(1), 3\u201320 (2016)","journal-title":"Ann. Math. Artif. Intell."},{"key":"385_CR33","volume-title":"Understanding and Using Linear Programming","author":"J Matousek","year":"2007","unstructured":"Matousek, J., G\u00e4rtner, B.: Understanding and Using Linear Programming. Springer, Berlin (2007)"},{"issue":"2","key":"385_CR34","doi-asserted-by":"publisher","first-page":"317","DOI":"10.1016\/0304-3975(91)90200-L","volume":"81","author":"N Megiddo","year":"1991","unstructured":"Megiddo, N., Papadimitriou, C.H.: On total functions, existence theorems and computational complexity. Theor. Comput. Sci. 81(2), 317\u2013324 (1991)","journal-title":"Theor. Comput. Sci."},{"key":"385_CR35","volume-title":"A Course in Game Theory","author":"MJ Osborne","year":"1994","unstructured":"Osborne, M.J., Rubinstein, A.: A Course in Game Theory. The MIT Press, Cambridge (1994)"},{"issue":"3","key":"385_CR36","doi-asserted-by":"publisher","first-page":"255","DOI":"10.2168\/LMCS-3(3:5)2007","volume":"3","author":"N Piterman","year":"2007","unstructured":"Piterman, N.: From nondeterministic B\u00fcchi and Streett automata to deterministic parity automata. Log. Methods Comput. Sci. 3(3), 255\u2013264 (2007)","journal-title":"Log. Methods Comput. Sci."},{"key":"385_CR37","doi-asserted-by":"crossref","unstructured":"Pnueli, A.: The temporal logic of programs. In: Proceedings of the Eighteenth IEEE Symposium on the Foundations of Computer Science, pp. 46\u201357 (1977)","DOI":"10.1109\/SFCS.1977.32"},{"key":"385_CR38","doi-asserted-by":"crossref","unstructured":"Pnueli, A., Rosner, R.: On the synthesis of a reactive module. In: POPL\u201989, pp. 179\u2013190. ACM (1989)","DOI":"10.1145\/75277.75293"},{"key":"385_CR39","unstructured":"Rosner, R.: Modular synthesis of reactive systems. Ph.D. Thesis, Weizmann (1991)"},{"key":"385_CR40","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511811654","volume-title":"Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations","author":"Y Shoham","year":"2008","unstructured":"Shoham, Y., Leyton-Brown, K.: Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations. Cambridge University Press, Cambridge (2008)"},{"key":"385_CR41","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511806292","volume-title":"Evolution and the Theory of Games","author":"JM Smith","year":"1982","unstructured":"Smith, J.M.: Evolution and the Theory of Games. Cambridge University Press, Cambridge (1982)"},{"issue":"2","key":"385_CR42","doi-asserted-by":"publisher","first-page":"146","DOI":"10.1137\/0201010","volume":"1","author":"RE Tarjan","year":"1972","unstructured":"Tarjan, R.E.: Depth-first search and linear graph algorithms. SIAM J. Comput. 1(2), 146\u2013160 (1972)","journal-title":"SIAM J. Comput."},{"key":"385_CR43","doi-asserted-by":"crossref","unstructured":"Ummels, M., Wojtczak, D.: The complexity of Nash equilibria in limit-average games. In: CONCUR\u201911, pp. 482\u2013496 (2011)","DOI":"10.1007\/978-3-642-23217-6_32"},{"key":"385_CR44","doi-asserted-by":"crossref","unstructured":"Vardi, M.Y.: An automata-theoretic approach to linear temporal logic. In: Logics for Concurrency\u2014Structure Versus Automata (8th Banff Higher Order Workshop, August 27\u2013September 3, 1995, Proceedings), pp. 238\u2013266 (1995)","DOI":"10.1007\/3-540-60915-6_6"},{"key":"385_CR45","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1016\/j.ic.2015.03.001","volume":"241","author":"Y Velner","year":"2015","unstructured":"Velner, Y., Chatterjee, K., Doyen, L., Henzinger, T.A., Rabinovich, A.M., Raskin, J.-F.: The complexity of multi-mean-payoff and multi-energy games. Inf. Comput. 241, 177\u2013196 (2015)","journal-title":"Inf. Comput."},{"key":"385_CR46","doi-asserted-by":"publisher","first-page":"418","DOI":"10.1016\/j.artint.2012.11.003","volume":"195","author":"M Wooldridge","year":"2013","unstructured":"Wooldridge, M., Endriss, U., Kraus, S., Lang, J.: Incentive engineering for Boolean games. Artif. Intell. 195, 418\u2013439 (2013)","journal-title":"Artif. Intell."},{"key":"385_CR47","doi-asserted-by":"crossref","unstructured":"Wooldridge, M., Gutierrez, J., Harrenstein, P., Marchioni, E., Perelli, G., Toumi, A.: Rational verification: from model checking to equilibrium checking. In: AAAI\u201916, pp. 4184\u20134191 (2016)","DOI":"10.1609\/aaai.v30i1.9878"},{"issue":"1&2","key":"385_CR48","doi-asserted-by":"publisher","first-page":"343","DOI":"10.1016\/0304-3975(95)00188-3","volume":"158","author":"U Zwick","year":"1996","unstructured":"Zwick, U., Paterson, M.: The complexity of mean payoff games on graphs. TCS 158(1&2), 343\u2013359 (1996)","journal-title":"TCS"}],"container-title":["Acta Informatica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00236-020-00385-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00236-020-00385-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00236-020-00385-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,10,28]],"date-time":"2022-10-28T05:47:49Z","timestamp":1666936069000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00236-020-00385-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,6,13]]},"references-count":48,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2021,12]]}},"alternative-id":["385"],"URL":"https:\/\/doi.org\/10.1007\/s00236-020-00385-4","relation":{},"ISSN":["0001-5903","1432-0525"],"issn-type":[{"value":"0001-5903","type":"print"},{"value":"1432-0525","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,6,13]]},"assertion":[{"value":"14 January 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 May 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 June 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}