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Rationality and solutions to nonconvex bargaining problems: rationalizability and Nash solutions. (English) Zbl 1280.91088
Summary: Conditions $${\alpha}$$ and $${\beta}$$ are two well-known rationality conditions in the theory of rational choice. This paper examines the implications of weaker versions of these two rationality conditions in the context of solutions to nonconvex bargaining problems. It is shown that, together with the standard axioms of efficiency and strict individual rationality, they imply rationalizability of solutions to nonconvex bargaining problems. We then characterize asymmetric Nash solutions by imposing a continuity and the scale invariance requirements. These results make a further connection between solutions to nonconvex bargaining problems and rationalizability of choice function in the theory of rational choice.

##### MSC:
 91B26 Auctions, bargaining, bidding and selling, and other market models 91B06 Decision theory 91A26 Rationality and learning in game theory
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