Farsighted house allocation

In this note we study von neumann–morgenstern farsightedly stable sets for shapley and scarf (1974) housing markets. Kawasaki (2010) shows that the set of competitive allocations coincides with the unique von neumann–morgenstern stable set based on a farsighted version of antisymmetric weak dominance (cf., wako, 1999). We demonstrate that the set of competitive allocations also coincides with the unique von neumann–morgenstern stable set based on a farsighted version of strong dominance (cf., roth and postlewaite, 1977) if no individual is indifferent between his endowment and the endowment of someone else.