Symmetric revealed cores and pseudocores, and Lawvere-Tierney closure operators
AbstractA 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.
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Bibliographic InfoPaper provided by Department of Economics, University of Siena in its series Department of Economics University of Siena with number 602.
Date of creation: Oct 2010
Date of revision:
Choice function; game solution; core; pseudocore; symmetric digraph; Lawvere-Tierney closure;
Find related papers by JEL classification:
- C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
- C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
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- D03 - Microeconomics - - General - - - Behavioral Microeconomics; Underlying Principles
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-12-11 (All new papers)
- NEP-GTH-2010-12-11 (Game Theory)
- NEP-ORE-2010-12-11 (Operations Research)
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