(Sophisticated) Stable Sets in Exchange Economies

Within the framework of (pure) exchange economies, we demonstrate that the von Neumann and Morgenstern stable set in the allocation space may differ from that in the corresponding utility space. Following Harsanyi (1974, Management Sci.20, 1472–1495), we then define the notion of the sophisticated stable set and establish an equivalence theorem: like the core, the sophisticated stable set in the allocation space coincides with that in the utility space. We also show that the sophisticated stable set has the desirable property of individual rationality. Journal of Economic Literature Classification Numbers: D51, C70, C71