  We formulate a general class of allocation problems called categorized domain
allocation problems (CDAPs), where indivisible items from multiple categories
are allocated to agents without monetary transfer and each agent gets at least
one item per category.
  We focus on basic CDAPs, where the number of items in each category is equal
to the number of agents. We characterize serial dictatorships for basic CDAPs
by a minimal set of three axiomatic properties: strategy-proofness,
non-bossiness, and category-wise neutrality. Then, we propose a natural
extension of serial dictatorships called categorial sequential allocation
mechanisms (CSAMs), which allocate the items in multiple rounds: in each round,
the active agent chooses an item from a designated category. We fully
characterize the worst-case rank efficiency of CSAMs for optimistic and
pessimistic agents, and provide a bound for strategic agents. We also conduct
experiments to compare expected rank efficiency of various CSAMs w.r.t. random
generated data.
