{"type":"ScholarlyArticle","title":"Exponential Lower Bounds on the Double Oracle Algorithm in Zero-Sum Games","authors":[{"name":"Brian Hu Zhang","slug":"brian-hu-zhang","given":"Brian Hu","family":"Zhang","affiliation":"Computer Science Department , Carnegie Mellon University"},{"name":"Tuomas Sandholm","slug":"tuomas-sandholm","given":"Tuomas","family":"Sandholm","affiliation":"Computer Science Department , Carnegie Mellon University; Strategy Robot, Inc.; Strategic Machine, Inc.; Optimized Markets, Inc."}],"abstract":"The double oracle algorithm is a popular method of solving games, because it is able to reduce computing equilibria to computing a series of best responses. However, its theoretical properties are not well understood. In this paper, we provide exponential lower bounds on the performance of the double oracle algorithm in both partially-observable stochastic games (POSGs) and extensive-form games (EFGs). Our results depend on what is assumed about the tiebreaking scheme---that is, which meta-Nash equilibrium or best response is chosen, in the event that there are multiple to pick from. In particular, for EFGs, our lower bounds require adversarial tiebreaking, whereas for POSGs, our lower bounds apply regardless of how ties are broken.","doi":"10.24963/ijcai.2024/336","url":"https://ijcai.org/proceedings/2024/336","pdf":"https://ijcai.org/proceedings/2024/0336.pdf","markdown":"https://ijcai.org/proceedings/2024/336.md","bibtex":"https://ijcai.org/proceedings/2024/bibtex/336","volume":{"slug":"2024","title":"Proceedings of the Thirty-Third International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2024","url":"https://ijcai.org/proceedings/2024/","year":2024,"location":"Jeju, Korea","dates":"3-9 August 2024","editors":"Kate Larson","isbn":"978-1-956792-04-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2024"},"section":"Game Theory and Economic Paradigms","track":"Main Track","number":336,"pages":{"first":3032,"last":3039},"keywords":["Game Theory and Economic Paradigms: GTEP: Noncooperative games"],"videos":[],"references":[{"position":1,"raw":"[Abernethy et al., 2021] Jacob Abernethy, Kevin A Lai, and Andre Wibisono. 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