{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/a-partial-state-space-model-of-unawareness","title":"A partial-state space model of unawareness","arxiv_id":"2412.00897","date":"2024-12-01","proceeding":null,"authors":["Wesley H. Holliday"],"abstract":"We propose a model of unawareness that remains close to the paradigm of Aumann's model for knowledge [R. J. Aumann, International Journal of Game Theory 28 (1999) 263-300]: just as Aumann uses a correspondence on a state space to define an agent's knowledge operator on events, we use a correspondence on a state space to define an agent's awareness operator on events. This is made possible by three ideas. First, like the model of [A. Heifetz, M. Meier, and B. Schipper, Journal of Economic Theory 130 (2006) 78-94], ours is based on a space of partial specifications of the world, partially ordered by a relation of further specification or refinement, and the idea that agents may be aware of some coarser-grained specifications while unaware of some finer-grained specifications; however, our model is based on a different implementation of this idea, related to forcing in set theory. Second, we depart from a tradition in the literature, initiated by [S. Modica and A. Rustichini, Theory and Decision 37 (1994) 107-124] and adopted by Heifetz et al. and [J. Li, Journal of Economic Theory 144 (2009) 977-993], of taking awareness to be definable in terms of knowledge. Third, we show that the negative conclusion of a well-known impossibility theorem concerning unawareness in [Dekel, Lipman, and Rustichini, Econometrica 66 (1998) 159-173] can be escaped by a slight weakening of a key axiom. Together these points demonstrate that a correspondence on a partial-state space is sufficient to model unawareness of events. Indeed, we prove a representation theorem showing that any abstract Boolean algebra equipped with awareness, knowledge, and belief operators satisfying some plausible axioms is representable as the algebra of events arising from a partial-state space with awareness, knowledge, and belief correspondences.","url_abs":"https://arxiv.org/abs/2412.00897v2","url_pdf":"https://arxiv.org/pdf/2412.00897v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"a-partial-state-space-model-of-unawareness","repo_url":"https://github.com/wesholliday/awareness","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"model","task_name":"model"}],"methods":[{"method_slug":"aware","method_name":"AWARE"},{"method_slug":"set","method_name":"SET"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}