Rationality and Solutions to Nonconvex Bargaining Problems: Rationalizable, Asymmetric and Nash Solutions

Conditions α and β 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. We also give a characterization of the Nash solution by using the two rationality conditions. These results make a further connection between solutions to non-convex bargaining problems and rationalizability of choice function in the theory of rational choice.