Abstract
In this note we study von Neumann-Morgenstern farsightedly stable sets for Shapley and Scarf (1974) housing markets. Kawasaki (2008) 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.