We investigate general properties of weak domination in the Shapley-Scarf exchange model with indivisible goods. We prove that every weakly dominated allocation is weakly dominated by some competitive allocation. Furthermore, if an allocation does not weakly dominate some other allocation, it is a weakly dominated allocation or the two allocations are indifferent. By using these results, we show that every non-competitive allocation is weakly dominated by some competitive allocation. The nonempty strong core proves to be a von Neumann-Morgenstern solution. We give also a necessary and sufficient condition for the equivalence of the strong core and the competitive allocations.