{"type":"ScholarlyArticle","title":"Discounting in Strategy Logic","authors":[{"name":"Munyque Mittelmann","slug":"munyque-mittelmann","given":"Munyque","family":"Mittelmann","affiliation":"University of Naples \"Federico II\""},{"name":"Aniello Murano","slug":"aniello-murano","given":"Aniello","family":"Murano","affiliation":"University of Naples \"Federico II\""},{"name":"Laurent Perrussel","slug":"laurent-perrussel","given":"Laurent","family":"Perrussel","affiliation":"University of Toulouse -IRIT"}],"abstract":"Discounting is an important dimension in multi-agent systems as long as we want to reason about strategies and time. It is a key aspect in economics as it captures the intuition that the far-away future is not as important as the near future. Traditional verification techniques allow to check whether there is a winning strategy for a group of agents but they do not take into account the fact that satisfying a goal sooner is different from satisfying it after a long wait. \r\nIn this paper, we augment Strategy Logic with future discounting over a set of discounted functions D, denoted SL[D]. We consider “until” operators with discounting functions: the satisfaction value of a specification in SL[D] is a value in [0, 1], where the longer it takes to fulfill requirements, the smaller the satisfaction value is. We motivate our approach with classical examples from Game Theory and study the complexity of model-checking SL[D]-formulas.","doi":"10.24963/ijcai.2023/26","url":"https://ijcai.org/proceedings/2023/26","pdf":"https://ijcai.org/proceedings/2023/0026.pdf","markdown":"https://ijcai.org/proceedings/2023/26.md","bibtex":"https://ijcai.org/proceedings/2023/bibtex/26","volume":{"slug":"2023","title":"Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2023","url":"https://ijcai.org/proceedings/2023/","year":2023,"location":"Macao, SAR","dates":"19-25 August 2023","editors":"Edith Elkind","isbn":"978-1-956792-03-4","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2023"},"section":"Agent-based and Multi-agent Systems","track":"Main Track","number":26,"pages":{"first":225,"last":233},"keywords":["Agent-based and Multi-agent Systems: MAS: Formal verification, validation and synthesis","Knowledge Representation and Reasoning: KRR: Qualitative, geometric, spatial, and temporal reasoning","Knowledge Representation and Reasoning: KRR: Computational complexity of reasoning"],"videos":[],"references":[{"position":1,"raw":"[Abreu, 1988] Dilip Abreu. On the theory of infinitely re- peated games with discounting. Econometrica: Journal of the Econometric Society, pages 383-396, 1988.","title":"On the theory of infinitely repeated games with discounting","authors":"Dilip Abreu","year":"1988","venue":"Econometrica: Journal of the Econometric Society","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Alechina et al., 2017] Natasha Alechina, Brian Logan, Hoang Nga Nguyen, and Franco Raimondi. Model- checking for resource-bounded ATL with production and consumption of resources. J. Comput. Syst. Sci., 88:126- 144, 2017.","title":"Modelchecking for resource-bounded ATL with production and consumption of resources","authors":"Natasha Alechina, Brian Logan, Nga Hoang, Franco Nguyen, Raimondi","year":"2017","venue":"J. Comput. Syst. Sci","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Alechina et al., 2018] Natasha Alechina, Nils Bulling, Stéphane Demri, and Brian Logan. On the complexity of resource-bounded logics. Theor. Comput. Sci., 750:69- 100, 2018.","title":"On the complexity of resource-bounded logics","authors":"Natasha Alechina, Nils Bulling, Stéphane Demri, Brian Logan","year":"2018","venue":"Theor. Comput. Sci","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Almagor et al., 2014] Shaull Almagor, Udi Boker, and Orna Kupferman. Discounting in LTL. In Proc. of TACAS, 2014.","title":"Discounting in LTL","authors":"Shaull Almagor, Udi Boker, Orna Kupferman","year":"2014","venue":"Proc. of TACAS","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Almagor et al., 2016] Shaull Almagor, Udi Boker, and Orna Kupferman. Formally reasoning about quality. Journal of the ACM, 63(3):1-56, 2016.","title":"Formally reasoning about quality","authors":"Shaull Almagor, Udi Boker, Orna Kupferman","year":"2016","venue":"Journal of the ACM","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Alur et al., 2002] Rajeev Alur, Thomas A. Henzinger, and Orna Kupferman. Alternating-time temporal logic. Jour- nal of the ACM, 49(5):672-713, 2002.","title":"Alternating-time temporal logic","authors":"Rajeev Alur, Thomas A Henzinger, Orna Kupferman","year":"2002","venue":"Journal of the ACM","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Aminof et al., 2016] Benjamin Aminof, Aniello Murano, Sasha Rubin, and Florian Zuleger. Prompt alternating-time epistemic logics. In Proc. of KR, 2016.","title":"Prompt alternating-time epistemic logics","authors":"Benjamin Aminof, Aniello Murano, Sasha Rubin, Florian Zuleger","year":"2016","venue":"Proc. of KR","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Babaioff et al., 2009] Moshe Babaioff, Michael Dinitz, Anupam Gupta, Nicole Immorlica, and Kunal Talwar. Sec- retary problems: weights and discounts. In Proc. of SODA, 2009.","title":"Secretary problems: weights and discounts","authors":"Moshe Babaioff, Michael Dinitz, Anupam Gupta, Nicole Immorlica, Kunal Talwar","year":"2009","venue":"Proc. of SODA","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Belardinelli et al., 2020] Francesco Belardinelli, Alessio Lomuscio, Aniello Murano, and Sasha Rubin. Verification of multi-agent systems with public actions against strategy logic. Artificial Intelligence, 285, 2020.","title":"Verification of multi-agent systems with public actions against strategy logic","authors":"Francesco Belardinelli, Alessio Lomuscio, Aniello Murano, Sasha Rubin","year":"2020","venue":"Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Berthon et al., 2021] Raphaël Berthon, Bastien Maubert, Aniello Murano, Sasha Rubin, and Moshe Y. Vardi. Strat- egy logic with imperfect information. ACM Trans. Com- put. Logic, 22(1), 2021.","title":"Strategy logic with imperfect information","authors":"Raphaël Berthon, Bastien Maubert, Aniello Murano, Sasha Rubin, Moshe Y Vardi","year":"2021","venue":"ACM Trans. Comput. Logic","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Bohy et al., 2013] Aaron Bohy, Véronique Bruyère, Em- manuel Filiot, and Jean-François Raskin. Synthesis from LTL specifications with mean-payoff objectives. In Proc. of TACAS, 2013.","title":"Synthesis from LTL specifications with mean-payoff objectives","authors":"Aaron Bohy, Véronique Bruyère, Emmanuel Filiot, Jean-François Raskin","year":"2013","venue":"Proc. of TACAS","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Bouyer et al., 2008] Patricia Bouyer, Ulrich Fahrenberg, Kim Guldstrand Larsen, Nicolas Markey, and Jirí Srba. Infinite runs in weighted timed automata with energy con- straints. In Proc. of FORMATS, 2008.","title":"Infinite runs in weighted timed automata with energy constraints","authors":"Patricia Bouyer, Ulrich Fahrenberg, Kim Guldstrand Larsen, Nicolas Markey, Jirí Srba","year":"2008","venue":"Proc. of FORMATS","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Bouyer et al., 2014] Patricia Bouyer, Nicolas Markey, and Raj Mohan Matteplackel. Averaging in LTL. In Proc. of CONCUR, 2014.","title":"Averaging in LTL","authors":"Patricia Bouyer, Nicolas Markey, Raj Mohan Matteplackel","year":"2014","venue":"Proc. of CONCUR","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Bouyer et al., 2019] Patricia Bouyer, Orna Kupferman, Nicolas Markey, Bastien Maubert, Aniello Murano, and Giuseppe Perelli. Reasoning about quality and fuzziness of strategic behaviours. In Proc. of IJCAI, 2019.","title":"Reasoning about quality and fuzziness of strategic behaviours","authors":"Patricia Bouyer, Orna Kupferman, Nicolas Markey, Bastien Maubert, Aniello Murano, Giuseppe Perelli","year":"2019","venue":"Proc. of IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2019/220"},{"position":15,"raw":"[Bouyer et al., 2023] Patricia Bouyer, Orna Kupferman, Nicolas Markey, Bastien Maubert, Aniello Murano, and Giuseppe Perelli. Reasoning about quality and fuzziness of strategic behaviors. ACM Trans. Comput. Logic, 24(3), 2023.","title":"Reasoning about quality and fuzziness of strategic behaviors","authors":"Patricia Bouyer, Orna Kupferman, Nicolas Markey, Bastien Maubert, Aniello Murano, Giuseppe Perelli","year":"2023","venue":"ACM Trans. Comput. Logic","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Bozzone and Naumov, 2021] Lia Bozzone and Pavel Nau- mov. Budget-constrained coalition strategies with dis- counting. Journal of Logic and Computation, 32(4):832- 851, 12 2021.","title":"Budget-constrained coalition strategies with discounting","authors":"Lia Bozzone, Pavel Naumov","year":"2021","venue":"Journal of Logic and Computation","doi":null,"url":null,"internal_url":"/proceedings/2021/249"},{"position":17,"raw":"[Brihaye et al., 2007] Thomas Brihaye, François Larous- sinie, Nicolas Markey, and Ghassan Oreiby. Timed con- current game structures. In Proc. of CONCUR, 2007.","title":"Timed concurrent game structures","authors":"Thomas Brihaye, François Laroussinie, Nicolas Markey, Ghassan Oreiby","year":"2007","venue":"Proc. of CONCUR","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Bulling and Goranko, 2022] Nils Bulling and Valentin Goranko. Combining quantitative and qualitative reason- ing in concurrent multi-player games. Auton. Agents Multi Agent Syst., 36(1):2, 2022.","title":"Combining quantitative and qualitative reasoning in concurrent multi-player games","authors":"Goranko Bulling, Nils Bulling, Valentin Goranko","year":"2022","venue":"Auton. Agents Multi Agent Syst","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Cermák et al., 2018] Petr Cermák, Alessio Lomuscio, Fabio Mogavero, and Aniello Murano. Practical verifi- cation of multi-agent systems against SLK specifications. Inf. Comput., 261:588-614, 2018.","title":"Practical verification of multi-agent systems against SLK specifications","authors":"Cermák","year":"2018","venue":"Inf. Comput","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Chakrabarti et al., 2003] Arindam Chakrabarti, Luca de Al- faro, Thomas A. Henzinger, and Mariëlle Stoelinga. Re- source interfaces. In Proc. of EMSOFT, 2003.","title":"Resource interfaces","authors":"Arindam Chakrabarti, Thomas A Luca De Alfaro, Mariëlle Henzinger, Stoelinga","year":"2003","venue":"Proc. of EMSOFT","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Chatterjee et al., 2010] Krishnendu Chatterjee, Thomas A Henzinger, and Nir Piterman. Strategy Logic. Inf. Com- put., 208(6):677-693, 2010.","title":"Strategy Logic","authors":"Krishnendu Chatterjee, Thomas A Henzinger, Nir Piterman","year":"2010","venue":"Inf. Comput","doi":null,"url":null,"internal_url":null},{"position":22,"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 Syst. Des., 43(1):61-92, 2013.","title":"Automatic verification of competitive stochastic systems","authors":"Chen","year":"2013","venue":"Formal Methods Syst. Des","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Clarke et al., 2018] Edmund M Clarke, Thomas A Hen- zinger, Helmut Veith, Roderick Bloem, et al. Handbook of model checking, volume 10. Springer, 2018.","title":"Handbook of model checking","authors":"Edmund M Clarke, Thomas A Henzinger, Helmut Veith, Roderick Bloem","year":"2018","venue":null,"doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[De Alfaro et al., 2003] Luca De Alfaro, Thomas A Hen- zinger, and Rupak Majumdar. Discounting the future in systems theory. In Proc. of ICALP, 2003.","title":"Discounting the future in systems theory","authors":"Luca De Alfaro, Thomas A Henzinger, Rupak Majumdar","year":"2003","venue":"Proc. of ICALP","doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[De Alfaro et al., 2005] Luca De Alfaro, Marco Faella, Thomas A Henzinger, Rupak Majumdar, and Mariëlle Stoelinga. Model checking discounted temporal proper- ties. Theor. Comput. Sci., 345(1):139-170, 2005.","title":"Model checking discounted temporal properties","authors":"Luca De Alfaro, Marco Faella, Thomas A Henzinger, Rupak Majumdar, Mariëlle Stoelinga","year":"2005","venue":"Theor. Comput. Sci","doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[Do et al., 2022] Virginie Do, Matthieu Hervouin, Jérôme Lang, and Piotr Skowron. Online approval committee elections. In Proc. of IJCAI, 2022.","title":"Online approval committee elections","authors":"Virginie Do, Matthieu Hervouin, Jérôme Lang, Piotr Skowron","year":"2022","venue":"Proc. of IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2022/36"},{"position":27,"raw":"[Ehrenfeucht and Mycielski, 1979] Andrzej Ehrenfeucht and Jan Mycielski. Positional strategies for mean payoff games. Int. Journal of Game Theory, 8(2):109-113, 1979.","title":"Positional strategies for mean payoff games","authors":"Andrzej Ehrenfeucht, Jan Mycielski","year":"1979","venue":"Int. Journal of Game Theory","doi":null,"url":null,"internal_url":null},{"position":28,"raw":"[Emerson and Jutla, 1991] E. Allen Emerson and Charan- jit S. Jutla. Tree automata, mu-calculus and determinacy. In Proc. of FOCS, 1991.","title":"Tree automata, mu-calculus and determinacy","authors":"E, Allen Emerson, Charanjit S Jutla","year":"1991","venue":"Proc. of FOCS","doi":null,"url":null,"internal_url":null},{"position":29,"raw":"[Fatima et al., 2006] Shaheen Fatima, Michael Wooldridge, and Nicholas Jennings. Multi-issue negotiation with dead- lines. J. Artif. Intell. Res., 27:381-417, 2006.","title":"Multi-issue negotiation with deadlines","authors":"Shaheen Fatima, Michael Wooldridge, Nicholas Jennings","year":"2006","venue":"J. Artif. Intell. Res","doi":null,"url":null,"internal_url":null},{"position":30,"raw":"[Fijalkow et al., 2020] Nathanaël Fijalkow, Bastien Maubert, Aniello Murano, and Moshe Y. Vardi. Assume- guarantee synthesis for prompt linear temporal logic. In In Proc. of IJCAI, 2020.","title":"Assumeguarantee synthesis for prompt linear temporal logic","authors":"Nathanaël Fijalkow, Bastien Maubert, Aniello Murano, Moshe Y Vardi","year":"2020","venue":"Proc. of IJCAI","doi":null,"url":null,"internal_url":null},{"position":31,"raw":"[Filar and Vrieze, 1996] Jerzy Filar and Koos Vrieze. Com- petitive Markov Decision Processes. Springer-Verlag, Berlin, Heidelberg, 1996.","title":"Competitive Markov Decision Processes","authors":"Vrieze Filar, Jerzy Filar, Koos Vrieze","year":"1996","venue":null,"doi":null,"url":null,"internal_url":null},{"position":32,"raw":"[Freeman, 1983] P.R. Freeman. The secretary problem and its extensions: A review. Int. Statistical Review/Revue Int. e de Statistique, pages 189-206, 1983.","title":"The secretary problem and its extensions: A review","authors":"P R Freeman","year":"1983","venue":"Int. Statistical Review/Revue Int. e de Statistique","doi":null,"url":null,"internal_url":null},{"position":33,"raw":"[Fudenberg and Maskin, 1990] Drew Fudenberg and Eric Maskin. Nash and perfect equilibria of discounted re- peated games. J. of Econ, Theory, 51(1):194-206, 1990.","title":"Nash and perfect equilibria of discounted repeated games","authors":"Maskin Fudenberg, Eric Maskin","year":"1990","venue":"J. of Econ, Theory","doi":null,"url":null,"internal_url":null},{"position":34,"raw":"[Fudenberg and Maskin, 2009] Drew Fudenberg and Eric Maskin. The folk theorem in repeated games with dis- counting or with incomplete information. In A long-run collaboration on long-run games. World Scientific, 2009.","title":"The folk theorem in repeated games with discounting or with incomplete information","authors":"Maskin Fudenberg, Drew Fudenberg, Eric Maskin","year":"2009","venue":"A long-run collaboration on long-run games","doi":null,"url":null,"internal_url":null},{"position":35,"raw":"[Grädel et al., 2002] Erich Grädel, Wolfgang Thomas, and Thomas Wilke. Automata, logics, and infinite games: a guide to current research, volume 2500. Springer Science & Business Media, 2002.","title":"Automata, logics, and infinite games: a guide to current research","authors":"Grädel","year":"2002","venue":null,"doi":null,"url":null,"internal_url":null},{"position":36,"raw":"[Gutierrez et al., 2021] Julian Gutierrez, Aniello Murano, Giuseppe Perelli, Sasha Rubin, Thomas Steeples, and Michael J. Wooldridge. Equilibria for games with com- bined qualitative and quantitative objectives. Acta Infor- matica, 58(6):585-610, 2021.","title":"Equilibria for games with combined qualitative and quantitative objectives","authors":"Julian Gutierrez, Aniello Murano, Giuseppe Perelli, Sasha Rubin, Thomas Steeples, Michael J Wooldridge","year":"2021","venue":"Acta Informatica","doi":null,"url":null,"internal_url":null},{"position":37,"raw":"[Harris and Madden, 2002] Andrew C Harris and Gregory J Madden. Delay discounting and performance on the prisoner's dilemma game. The Psychological Record, 52(4):429-440, 2002.","title":"Delay discounting and performance on the prisoner's dilemma game","authors":"C Andrew, Gregory J Harris, Madden","year":"2002","venue":"The Psychological Record","doi":null,"url":null,"internal_url":null},{"position":38,"raw":"[Henzinger and Prabhu, 2006] Thomas A. Henzinger and Vinayak S. Prabhu. Timed alternating-time temporal logic. In Proc. of FORMATS, 2006.","title":"Timed alternating-time temporal logic","authors":"Thomas A Henzinger, S Vinayak, Prabhu","year":"2006","venue":"Proc. of FORMATS","doi":null,"url":null,"internal_url":null},{"position":39,"raw":"[Jamroga et al., 2020] Wojciech Jamroga, Beata Konikowska, Damian Kurpiewski, and Wojciech Penczek. Multi-valued verification of strategic ability. Fundam. Informaticae, 175(1-4):207-251, 2020.","title":"Multi-valued verification of strategic ability","authors":"Wojciech Jamroga, Beata Konikowska, Damian Kurpiewski, Wojciech Penczek","year":"2020","venue":"Fundam. Informaticae","doi":null,"url":null,"internal_url":null},{"position":40,"raw":"[Jamroga, 2008a] Wojciech Jamroga. A temporal logic for markov chains. In Proc. of AAMAS, 2008.","title":"Wojciech Jamroga. A temporal logic for markov chains","authors":"Jamroga","year":"2008","venue":"Proc. of AAMAS","doi":null,"url":null,"internal_url":null},{"position":41,"raw":"[Jamroga, 2008b] Wojciech Jamroga. A temporal logic for stochastic multi-agent systems. In Proc. of PRIMA, 2008.","title":"Wojciech Jamroga. A temporal logic for stochastic multi-agent systems","authors":"Jamroga","year":"2008","venue":"Proc. of PRIMA","doi":null,"url":null,"internal_url":null},{"position":42,"raw":"[Kupferman et al., 2000] Orna Kupferman, Moshe Y Vardi, and Pierre Wolper. An automata-theoretic approach to branching-time model checking. Journal of the ACM, 47(2):312-360, 2000.","title":"An automata-theoretic approach to branching-time model checking","authors":"Orna Kupferman, Moshe Y Vardi, Pierre Wolper","year":"2000","venue":"Journal of the ACM","doi":null,"url":null,"internal_url":null},{"position":43,"raw":"[Laroussinie et al., 2006] François Laroussinie, Nicolas Markey, and Ghassan Oreiby. Model-checking timed. In Proc. of FORMATS, 2006.","title":"Model-checking timed","authors":"François Laroussinie, Nicolas Markey, Ghassan Oreiby","year":"2006","venue":"Proc. of FORMATS","doi":null,"url":null,"internal_url":null},{"position":44,"raw":"[Livne, 1979] Zvi A Livne. The role of time in negotiations. PhD thesis, Massachusetts Institute of Technology, 1979.","title":"The role of time in negotiations","authors":"A Zvi, Livne","year":"1979","venue":null,"doi":null,"url":null,"internal_url":null},{"position":45,"raw":"[Locey et al., 2013] Matthew L Locey, Vasiliy Safin, and Howard Rachlin. Social discounting and the prisoner's dilemma game. Journal of the experimental analysis of behavior, 99(1):85-97, 2013.","title":"Social discounting and the prisoner's dilemma game","authors":"Vasiliy Matthew L Locey, Howard Safin, Rachlin","year":"2013","venue":"Journal of the experimental analysis of behavior","doi":null,"url":null,"internal_url":null},{"position":46,"raw":"[Mandrali, 2012] Eleni Mandrali. Weighted LTL with dis- counting. In Proc. of CIAA, 2012.","title":"Eleni Mandrali. Weighted LTL with discounting","authors":"Mandrali","year":"2012","venue":"Proc. of CIAA","doi":null,"url":null,"internal_url":null},{"position":47,"raw":"[Maubert et al., 2021] Bastien Maubert, Munyque Mittel- mann, Aniello Murano, and Laurent Perrussel. Strategic reasoning in automated mechanism design. In Proc. of KR, 2021.","title":"Strategic reasoning in automated mechanism design","authors":"Bastien Maubert, Munyque Mittelmann, Aniello Murano, Laurent Perrussel","year":"2021","venue":"Proc. of KR","doi":null,"url":null,"internal_url":null},{"position":48,"raw":"[Mittelmann and Perrussel, 2020] Munyque Mittelmann and Laurent Perrussel. Auction description language (ADL): General framework for representing auction-based mar- kets. In Proc. of ECAI, 2020.","title":"Munyque Mittelmann and Laurent Perrussel. Auction description language (ADL): General framework for representing auction-based markets","authors":"Perrussel Mittelmann","year":"2020","venue":"Proc. of ECAI","doi":null,"url":null,"internal_url":null},{"position":49,"raw":"[Mittelmann et al., 2022] Munyque Mittelmann, Bastien Maubert, Aniello Murano, and Laurent Perrussel. Au- tomated synthesis of mechanisms. In Proc. of IJCAI, 2022.","title":"Automated synthesis of mechanisms","authors":"Mittelmann","year":"2022","venue":"Proc. of IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2022/61"},{"position":50,"raw":"[Mogavero et al., 2014] Fabio Mogavero, Aniello Murano, Giuseppe Perelli, and Moshe Y. Vardi. Reasoning about strategies: On the model-checking problem. ACM Trans. Comput. Log., 15(4), 2014.","title":"Reasoning about strategies: On the model-checking problem","authors":"Fabio Mogavero, Aniello Murano, Giuseppe Perelli, Moshe Y Vardi","year":"2014","venue":"ACM Trans. Comput. Log","doi":null,"url":null,"internal_url":null},{"position":51,"raw":"[Muller and Schupp, 1987] David E. Muller and Paul E. Schupp. Alternating automata on infinite trees. Theor. Comput. Sci., 54(2):267-276, 1987.","title":"Alternating automata on infinite trees","authors":"David E Muller, Paul E Schupp","year":"1987","venue":"Theor. Comput. Sci","doi":null,"url":null,"internal_url":null},{"position":52,"raw":"[Nisan et al., 2007] Noam Nisan, Tim Roughgarden, Eva Tardos, and Vijay V Vazirani. Algorithmic Game Theory. Cambridge University Press, 2007.","title":"Algorithmic Game Theory","authors":"Nisan","year":"2007","venue":null,"doi":null,"url":null,"internal_url":null},{"position":53,"raw":"[Pauly and Wooldridge, 2003] M. Pauly and M. Wooldridge. Logic for mechanism design-a manifesto. In Workshop on Game Theory and Decision Theory in Agent Syst., 2003.","title":"Logic for mechanism design-a manifesto","authors":"M Pauly, M Wooldridge","year":"2003","venue":"Workshop on Game Theory and Decision Theory in Agent Syst","doi":null,"url":null,"internal_url":null},{"position":54,"raw":"[Pęski, 2014] Marcin Pęski. Repeated games with incom- plete information and discounting. Theoretical Eco- nomics, 9(3):651-694, 2014.","title":"Marcin Pęski. Repeated games with incomplete information and discounting","authors":"Pęski","year":"2014","venue":"Theoretical Economics","doi":null,"url":null,"internal_url":null},{"position":55,"raw":"[Pnueli, 1977] Amir Pnueli. The temporal logic of programs. In Prof. of FOCS, 1977.","title":"The temporal logic of programs","authors":"Amir Pnueli, Pnueli","year":"1977","venue":"Prof. of FOCS","doi":null,"url":null,"internal_url":null},{"position":56,"raw":"[Rubinstein, 1982] Ariel Rubinstein. Perfect equilibrium in a bargaining model. Econometrica: Journal of the Econo- metric Society, pages 97-109, 1982.","title":"Ariel Rubinstein. Perfect equilibrium in a bargaining model","authors":"Rubinstein","year":"1982","venue":"Econometrica: Journal of the Econometric Society","doi":null,"url":null,"internal_url":null},{"position":57,"raw":"[Shapley, 1953] Lloyd S Shapley. Stochastic games. Proc. of national academy of sciences, 39(10):1095-1100, 1953.","title":"Stochastic games","authors":"S Lloyd, Shapley","year":"1953","venue":"Proc. of national academy of sciences","doi":null,"url":null,"internal_url":null},{"position":58,"raw":"[Thomas, 1990] Wolfgang Thomas. Automata on infinite ob- jects. In Formal Models and Semantics, pages 133-191. Elsevier, 1990.","title":"Automata on infinite objects","authors":"Wolfgang Thomas, Thomas","year":"1990","venue":"Formal Models and Semantics","doi":null,"url":null,"internal_url":null},{"position":59,"raw":"[Vardi and Wolper, 1986] Moshe Y Vardi and Pierre Wolper. An automata-theoretic approach to automatic program ver- ification. In Proc. of LICS, 1986.","title":"An automata-theoretic approach to automatic program verification","authors":"Wolper Vardi, Moshe Y Vardi, Pierre Wolper","year":"1986","venue":"Proc. of LICS","doi":null,"url":null,"internal_url":null},{"position":60,"raw":"[Vester, 2015] Steen Vester. On the complexity of model- checking branching and alternating-time temporal logics in one-counter systemss. In Proc. of ATVA, 2015.","title":"On the complexity of modelchecking branching and alternating-time temporal logics in one-counter systemss","authors":"Steen Vester","year":"2015","venue":"Proc. of ATVA","doi":null,"url":null,"internal_url":null},{"position":61,"raw":"[Weg et al., 1990] Eythan Weg, Amnon Rapoport, and Dan S Felsenthal. Two-person bargaining behavior in fixed dis- counting factors games with infinite horizon. Games and Economic Behavior, 2(1):76-95, 1990.","title":"Two-person bargaining behavior in fixed discounting factors games with infinite horizon","authors":"Weg","year":"1990","venue":"Games and Economic Behavior","doi":null,"url":null,"internal_url":null},{"position":62,"raw":"[Zwick and Paterson, 1996] Uri Zwick and Mike Paterson. The complexity of mean payoff games on graphs. Theor. Comput. Sci., 158(1&2):343-359, 1996.","title":"The complexity of mean payoff games on graphs","authors":"Paterson Zwick, Uri Zwick, Mike Paterson","year":"1996","venue":"Theor. Comput. Sci","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}