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Carvalho, L. (2021). Proportional bargaining solutions, strictly comprehensive sets and the axiom of continuity. Annals of Operations Research. 301, 41-53
L. C. Carvalho, "Proportional bargaining solutions, strictly comprehensive sets and the axiom of continuity", in Ann. of Operations Research, vol. 301, pp. 41-53, 2021
@article{carvalho2021_1715303882423, author = "Carvalho, L.", title = "Proportional bargaining solutions, strictly comprehensive sets and the axiom of continuity", journal = "Annals of Operations Research", year = "2021", volume = "301", number = "", doi = "10.1007/s10479-020-03595-8", pages = "41-53", url = "https://link.springer.com/article/10.1007/s10479-020-03595-8" }
TY - JOUR TI - Proportional bargaining solutions, strictly comprehensive sets and the axiom of continuity T2 - Annals of Operations Research VL - 301 AU - Carvalho, L. PY - 2021 SP - 41-53 SN - 0254-5330 DO - 10.1007/s10479-020-03595-8 UR - https://link.springer.com/article/10.1007/s10479-020-03595-8 AB - Continuity is an axiom of Kalai (Econometrica 45(7):1623–1630, 1977)’s and Roth (Econometrica 47(3):775–777, 1979b)’s characterizations of the proportional bargaining. In this paper we establish that, in the class of strictly comprehensive sets, continuity is a corollary of the other axioms. Consequently the proportional solution can be axiomatically defined in the class of strictly comprehensive sets without the axiom of continuity. We also show it is possible to tighten Kalai (1977)’s and Roth (1979b)’s axiomatization of the proportional bargaining solution, assuming a weaker version of the axiom of continuity. ER -