Weak versus strong domination in a market with indivisible goods

Abstract

The core of a market in indivisible goods can be defined in terms of strong domination or weak domination. The core defined by strong domination is always non-empty, but may contain points which are unstable in a dynamic sense. However, it is shown that there are always stable points in the core, and a characterization is obtained. The core defined by weak domination is always non-empty when there is no indifference, and has no instability problems. In this case, the core coincides with the unique competitive allocation.