Reasoning about Bounded Reasoning
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866910126793818112 |
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| author | Liu, Shuige Ziegler, Gabriel |
| author_facet | Liu, Shuige Ziegler, Gabriel |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_19737 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Reasoning about Bounded Reasoning Liu, Shuige Ziegler, Gabriel Theoretical Economics 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. |
| title | Reasoning about Bounded Reasoning |
| topic | Theoretical Economics |
| url | https://arxiv.org/abs/2506.19737 |