Abstract
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 (Econometrica 45(7):1623–1630, 1977)’s and Roth (Econometrica 47(3):775–777, 1979b)’s axiomatization of the proportional bargaining solution, assuming a weaker version of the axiom of continuity.
Highlights
T happen that some player diminishes his utility while all the others maintain theirs
The proportional solution can be axiomatically defined in the class of strictly comprehensive sets without the axiom of continuity
In this work we first show that when the bargaining class has only strictly comprehensive sets, the axiom of continuity is a consequence of the other axioms
Summary
T happen that some player diminishes his utility while all the others maintain theirs. Abstract Continuity is an axiom of Kalai (1977)’s and Roth (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. The proportional solution can be axiomatically defined in the class of strictly comprehensive sets without the axiom of continuity.
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