Strategy-Proof Allocation of Indivisible Goods among Couples

We consider the problem of allocating indivisible goods among couples. Agents in a couple share the indivisible good assigned to them. The main result is that an allocation rule is strategy-proof, neutral and non-bossy if and only if it is serially dictatorial. An allocation rule is serially dictatorial if there is a priority order of couples and a function that identifies who chooses in each couple, such that for all preference profiles, a good assigned to couple i is the best element according to the preference of the identified agent in couple i among the remaining goods when the couples with higher priorities have made their choice.