On the extension of binary relations in economic and game theories

Athanasios Andrikopoulos ()
Additional contact information
Athanasios Andrikopoulos: University of Patras

Decisions in Economics and Finance, 2019, vol. 42, issue 1, No 14, 277-285

Abstract: Abstract Szpilrajn’s extension theorem on binary relations and its strengthening by Dushnik and Miller are fundamental in economic and game theories. Szpilrajn’s result entails that each partial order extends to a linear order. Dushnik and Miller use Szpilrajn’s theorem to show that each partial order has a realizer. Since then, many authors utilize Szpilrajn’s theorem and the well-ordering principle to prove more general theorems on extending binary relations. The original extension theorems of Szpilrajn, Dushnik-Miller and Moulin-Weymark are called: Szpilrajn extension theorem, Dushnik-Miller extension theorem and Moulin-Weymark’s Pareto extension theorem respectively. The generalizations of these theorems are called: Szpilrajn-type extension theorem, Dushnik-Miller-type extension theorem and Moulin-Weymark’s Pareto-type extension theorem respectively. The presented results generalize well-known extension theorems in the literature.

Keywords: Extension theorems; Consistent binary relations; Intersection of binary relations; Realizer (search for similar items in EconPapers)
JEL-codes: C60 C70 D00 D60 D71 (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10203-018-0213-4 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

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:spr:decfin:v:42:y:2019:i:1:d:10.1007_s10203-018-0213-4

Ordering information: This journal article can be ordered from
http://www.springer. ... ry/journal/10203/PS2

DOI: 10.1007/s10203-018-0213-4

Access Statistics for this article

Decisions in Economics and Finance is currently edited by Paolo Ghirardato

More articles in Decisions in Economics and Finance from Springer, Associazione per la Matematica
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().