We adopt the notion of von Neumann-Morgenstern farsightedly stable sets to predict which matchings are possibly stable when agents are farsighted in one-to-one matching problems. We provide the characterization of von Neumann-Morgenstern farsightedly stable sets: a set of matchings is a von Neumann-Morgenstern farsightedly stable set if and only if it is a singleton set and its element is a cor...

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 t...

Using a bi-choice graph technique (Klaus and Klijn, 2009), we show that a matching for a roommate market indirectly dominates another matching if and only if no blocking pair of the former is matched in the latter (Proposition 1). Using this characterization of indirect dominance, we investigate von Neumann-Morgenstern farsightedly stable sets. We show that a singleton is von Neumann-Morgenster...

We analyze the aggregation problem without the assumption that individuals and society have fully determined and observable preferences. More precisely, we endow individuals and society with sets of possible von Neumann-Morgenstern utility functions over lotteries. We generalize the classical neutrality assumption to this setting and characterize the class of neutral social welfare function. Th...

Cooperative games and von Neumann-Morgenstern solution. Situations when all participants collaborate with each other is known as a cooperative game. One way to describe a cooperative game is to assign, to every subset S ⊆ N def = {1, . . . , n} of the set of all the participants, the value v(S) that describes what players from S can gain if they collaborate between themselves only. Such subsets...