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THE HEX GAME THEOREM AND THE ARROW IMPOSSIBILITY THEOREM: THE CASE OF WEAK ORDERS.
- Source :
- Metroeconomica; Feb2009, Vol. 60 Issue 1, p77-90, 14p, 7 Diagrams
- Publication Year :
- 2009
-
Abstract
- The Arrow impossibility theorem when individual preferences are weak orders is equivalent to the HEX game theorem. Because Gale showed that the Brouwer fixed point theorem is equivalent to the HEX game theorem, this paper indirectly shows the equivalence of the Brouwer fixed point theorem and the Arrow impossibility theorem. Chichilnisky showed the equivalence of her impossibility theorem and the Brouwer fixed point theorem, and Baryshnikov showed that the impossibility theorem by Chichilnisky and the Arrow impossibility theorem are very similar. Thus, Chichilnisky and Baryshnikov are precedents for the result—linking the Arrow impossibility theorem to a fixed point theorem. [ABSTRACT FROM AUTHOR]
- Subjects :
- HEX (Game)
THEORY
BOARD games
BROUWERIAN algebras
GAMES
GAMEBOARDS
Subjects
Details
- Language :
- English
- ISSN :
- 00261386
- Volume :
- 60
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Metroeconomica
- Publication Type :
- Academic Journal
- Accession number :
- 36142077
- Full Text :
- https://doi.org/10.1111/j.1467-999X.2008.00332.x