  A simple mechanism for allocating indivisible resources is sequential
allocation in which agents take turns to pick items. We focus on possible and
necessary allocation problems, checking whether allocations of a given form
occur in some or all mechanisms for several commonly used classes of sequential
allocation mechanisms. In particular, we consider whether a given agent
receives a given item, a set of items, or a subset of items for five natural
classes of sequential allocation mechanisms: balanced, recursively balanced,
balanced alternating, strictly alternating and all policies. We identify
characterizations of allocations produced balanced, recursively balanced,
balanced alternating policies and strictly alternating policies respectively,
which extend the well-known characterization by Brams and King [2005] for
policies without restrictions. In addition, we examine the computational
complexity of possible and necessary allocation problems for these classes.
