Reasoning about Bounded Reasoning

[2506.19737] Reasoning about Bounded Reasoning Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Economics > Theoretical Economics arXiv:2506.19737 (econ) [Submitted on 24 Jun 2025 ( v1 ), last revised 14 Apr 2026 (this version, v5)] Title: Reasoning about Bounded Reasoning Authors: Shuige Liu , Gabriel Ziegler View a PDF of the paper titled Reasoning about Bounded Reasoning, by Shuige Liu and 1 other authors View PDF HTML (experimental) Abstract: In experimental applications of bounded-reasoning models, behavior is often summarized by distributions of "levels". We argue that such summaries conflate two conceptually distinct dimensions: a player's type, capturing beliefs about what types their opponents might be, and the depth of higher-order reasoning about rationality. Distinguishing these dimensions matters for interpreting experimental evidence and for understanding when cross-environment variation should be read as changes in beliefs versus changes in cognitive depth, but existing frameworks provide no language to do so. We develop a unified framework by "lifting" static complete-information games into incomplete-information versions in which players are explicitly uncertain about opponents' types. Within this framework, bounded reasoning about opponents' types is represented by transparent first-order belief restrictions, while (higher-order) reasoning depth is captured by bounds on belief in rationality. We analyze three benchmark instances: downward rationalizability, a robust baseline, and two refinements, $\mathsf{L}$-rationalizability and $\mathsf{C}$-rationalizability, which provide epistemic foundations -- with an important nuance -- for classic level-$k$ and Cognitive Hierarchy, respectively, and clarify what "level-$k$" behavior can and cannot reveal about underlying reasoning processes. Subjects: Theoretical Economics (econ.TH) Cite as: arXiv:2506.19737 [econ.TH] (or arXiv:2506.19737v5 [econ.TH] for this version) https://doi.org/10.48550/arXiv.2506.19737 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Shuige Liu [ view email ] [v1] Tue, 24 Jun 2025 15:56:24 UTC (35 KB) [v2] Thu, 3 Jul 2025 14:29:44 UTC (35 KB) [v3] Thu, 31 Jul 2025 15:10:31 UTC (38 KB) [v4] Wed, 8 Oct 2025 14:27:01 UTC (40 KB) [v5] Tue, 14 Apr 2026 08:28:45 UTC (53 KB) Full-text links: Access Paper: View a PDF of the paper titled Reasoning about Bounded Reasoning, by Shuige Liu and 1 other authors View PDF HTML (experimental) TeX Source view license Current browse context: econ.TH < prev | next > new | recent | 2025-06 Change to browse by: econ References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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