Symmetric revealed cores and pseudocores, and Lawvere-Tierney closure operators

Stefano Vannucci ()

Department of Economics University of Siena from Department of Economics, University of Siena

Abstract: A choice function is a symmetric revealed core if there exists a symmetric irreflexive ‘dominance’ digraph such that choice sets consist precisely of the locally undominated outcomes of the latter. Symmetric revealed pseudocores are similarly defined by omitting the irreflexivity requirement on the underlying digraph. Lawvere-Tierney (LT) closure operators are those closure operators which are meet-homomorphic: they may be regarded as an algebraic representation of a geometric modality denoting ‘locally true’, and provide the mathematical backbone of a generalized version of so-called ‘Grothendieck topologies’ in categories. The classes of symmetric revealed cores and pseudocores are characterized, and their basic order-theoretic structure is studied. In particular, it is shown that their respective posets are sub-meet-semilattices of the canonical lattice of choice functions. An order duality theorem concerning the posets of symmetric revealed pseudocores and LT closure operators on a given ground set is also established.

Keywords: Choice function; game solution; core; pseudocore; symmetric digraph; Lawvere-Tierney closure (search for similar items in EconPapers)
JEL-codes: C70 C71 D01 D03 (search for similar items in EconPapers)
Date: 2010-10
New Economics Papers: this item is included in nep-gth and nep-ore
References: Add references at CitEc
Citations:

Downloads: (external link)
http://repec.deps.unisi.it/quaderni/602.pdf (application/pdf)

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:usi:wpaper:602

Access Statistics for this paper

More papers in Department of Economics University of Siena from Department of Economics, University of Siena Contact information at EDIRC.
Bibliographic data for series maintained by Fabrizio Becatti ().