Maximal-Element Rationalizability |
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Authors: | Walter?Bossert Yves?Sprumont Email author" target="_blank">Kotaro?SuzumuraEmail author |
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Institution: | (1) Département de Sciences Economiques and CIREQ, Université de Montréal, H3C 3J7, succursale Centre-ville, Montréal, QC, C.P. 6128, Canada;(2) Institute of Economic Research, Hitotsubashi University, Kunitachi Tokyo, 186-8603, Japan |
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Abstract: | We examine the maximal-element rationalizability of choice functions with arbitrary domains. While rationality formulated
in terms of the choice of greatest elements according to a rationalizing relation has been analyzed relatively thoroughly
in the earlier literature, this is not the case for maximal-element rationalizability, except when it coincides with greatest-element
rationalizability because of properties imposed on the rationalizing relation. We develop necessary and sufficient conditions
for maximal-element rationalizability by itself, and for maximal-element rationalizability in conjunction with additional
properties of a rationalizing relation such as reflexivity, completeness, P-acyclicity, quasi-transitivity, consistency and transitivity.
Financial support through grants from the Social Sciences and Humanities Research Council of Canada, the Fonds pour la Formation
de Chercheurs et l'Aide à la Recherche of Québec, and a Grant-in-Aid for Scientific Research for Priority Areas from the Ministry
of Education, Culture, Sports, Science and Technology of Japan is gratefully acknowledged. Thanks are also due to the editor
and the two referees for the opportunity to improve the exposition of this paper. |
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Keywords: | choice functions maximal-element rationalizability |
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