61c On the Non-Transferable Utility Value: A Comment on the Roth–Shafer Examples

In game theory, the term ‘‘solution concept’’ denotes a correspondence between games and outcomes (or sets of outcomes). Two familiar examples of solution concepts are the Nash Equilibrium Point and the Core. Both are successful tools of economic analysis: applied to a variety of contexts, they yield important and interesting results. The Core is particularly successful in classical1 market contexts. Another solution concept is Shapley’s value [47]; more generally,2 his Non-Transferable-Utility (NTU) value3 [49]. While not as well-known as the core, it is in some ways even more ‘‘successful’’: it has been applied to a broader variety of contexts, often yielding interesting results.4 Several years ago, A. Roth [43] constructed a class of examples in which, he argued, the NTU value looks strange and counterintuitive; specifically, in which there are very strong, compelling reasons leading to an alternative outcome, not consistent with the NTU value. He concluded that ‘‘at the very least, some modifications are required in the existing theory.’’ While far from universally accepted in the profession, Roth’s work has had a considerable echo. The main purpose of this paper is to rebut Roth’s. We make two points: