  In fair division of indivisible goods, using sequences of sincere choices (or
picking sequences) is a natural way to allocate the objects. The idea is as
follows: at each stage, a designated agent picks one object among those that
remain. Another intuitive way to obtain an allocation is to give objects to
agents in the first place, and to let agents exchange them as long as such
"deals" are beneficial. This paper investigates these notions, when agents have
additive preferences over objects, and unveils surprising connections between
them, and with other efficiency and fairness notions. In particular, we show
that an allocation is sequenceable iff it is optimal for a certain type of
deals, namely cycle deals involving a single object. Furthermore, any
Pareto-optimal allocation is sequenceable, but not the converse. Regarding
fairness, we show that an allocation can be envy-free and non-sequenceable, but
that every competitive equilibrium with equal incomes is sequenceable. To
complete the picture, we show how some domain restrictions may affect the
relations between these notions. Finally, we experimentally explore the links
between the scales of efficiency and fairness.
