Roth-Postlewaite stability and von Neumann-Morgenstern stability

In the framework of the indivisible goods market defined in Shapley and Scarf (1974), Roth and Postlewaite (1977) define an allocation to be (RP-)stable if no coalition of agents can benefit from a reallocation of goods after the allocation has been decided upon. In this paper, we show that the set of RP-stable allocations is the unique von Neumann-Morgenstern (vNM-) stable set of the following domination relation: an allocation y dominates x if there is a coalition S that blocks x using allocation y in the market with x as its initial endowment. This connection between the two stability concepts also carries over for the indivisible goods market with multiple types of Konishi et al. (2001).