{"type":"ScholarlyArticle","title":"The Computational Complexity of Single-Player Imperfect-Recall Games","authors":[{"name":"Emanuel Tewolde","slug":"emanuel-tewolde","given":"Emanuel","family":"Tewolde","affiliation":"Foundations of Cooperative AI Lab (FOCAL) , Carnegie Mellon University"},{"name":"Caspar Oesterheld","slug":"caspar-oesterheld","given":"Caspar","family":"Oesterheld","affiliation":"Foundations of Cooperative AI Lab (FOCAL) , Carnegie Mellon University"},{"name":"Vincent Conitzer","slug":"vincent-conitzer","given":"Vincent","family":"Conitzer","affiliation":"Foundations of Cooperative AI Lab (FOCAL) , Carnegie Mellon University; University of Oxford"},{"name":"Paul W. Goldberg","slug":"paul-w-goldberg","given":"Paul W.","family":"Goldberg","affiliation":"University of Oxford"}],"abstract":"We study single-player extensive-form games with imperfect recall, such as the Sleeping Beauty problem or the Absentminded Driver game. For such games, two natural equilibrium concepts have been proposed as alternative solution concepts to ex-ante optimality. One equilibrium concept uses generalized double halving (GDH) as a belief system and evidential decision theory (EDT), and another one uses generalized thirding (GT) as a belief system and causal decision theory (CDT). Our findings relate those three solution concepts of a game to solution concepts of a polynomial maximization problem: global optima, optimal points with respect to subsets of variables and Karush–Kuhn–Tucker (KKT) points. Based on these correspondences, we are able to settle various complexity-theoretic questions on the computation of such strategies. For ex-ante optimality and (EDT,GDH)-equilibria, we obtain NP-hardness and inapproximability, and for (CDT,GT)-equilibria we obtain CLS-completeness results.","doi":"10.24963/ijcai.2023/321","url":"https://ijcai.org/proceedings/2023/321","pdf":"https://ijcai.org/proceedings/2023/0321.pdf","markdown":"https://ijcai.org/proceedings/2023/321.md","bibtex":"https://ijcai.org/proceedings/2023/bibtex/321","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":"Game Theory and Economic Paradigms","track":"Main Track","number":321,"pages":{"first":2878,"last":2887},"keywords":["Knowledge Representation and Reasoning: KRR: Computational complexity of reasoning","Game Theory and Economic Paradigms: GTEP: Noncooperative games","Game Theory and Economic Paradigms: GTEP: Other","Uncertainty in AI: UAI: Decision and utility theory"],"videos":[],"references":[{"position":1,"raw":"[Babichenko and Rubinstein, 2021] Yakov Babichenko and Aviad Rubinstein. 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