Rationality and solutions to nonconvex bargaining problems: Rationalizability and Nash solutions

Conditions αα and ββ 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.

► We study rationalizability of solutions to nonconvex problems.
► Two weaker versions of conditions alpha and beta, BCalpha and BCbeta, are introduced.
► Under efficiency and strict individual rationality, rationalizability is equivalent to BCalpha and BCbeta.
► A weak continuity property is introduced for studying Nash solutions.
► Nash solutions are characterized by using this continuity property.