A partial-state space model of unawareness

Wesley H. Holliday

Journal of Mathematical Economics, 2025, vol. 116, issue C

Abstract: We propose a model of unawareness that remains close to the paradigm of Aumann’s (1999a) model for knowledge: 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 Heifetz, Meier, and Schipper (2006), 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 Modica and Rustichini (1994) and adopted by Heifetz et al. and Li (2009), 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 due to Dekel, Lipman, and Rustichini (1998) 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.

Keywords: Unawareness; Knowledge; Belief; Interactive epistemology (search for similar items in EconPapers)
JEL-codes: C70 C72 D80 D83 (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304406824001411
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:mateco:v:116:y:2025:i:c:s0304406824001411

DOI: 10.1016/j.jmateco.2024.103081

Access Statistics for this article

Journal of Mathematical Economics is currently edited by Atsushi (A.) Kajii

More articles in Journal of Mathematical Economics from Elsevier
Bibliographic data for series maintained by Catherine Liu ().