Assigning indivisible and categorized items

In this paper, we study the problem of assigning indivisible items under the following constraints: 1) each item belongs to one of the p categories, 2) each agent is required to get exactly one item from each category, 3) no free disposal, and 4) no monetary transfer. We first characterize serial dictatorships by a minimal set of 3 properties: strategy-proofness, non-bossiness, and categorywise neutrality. Then, we analyze a natural extension of serial dictatorships called sequential allocation mechanisms, which allocates the items in muitple stages according to a given order over all (agent,category) pairs, so that in each stage, the designated agent chooses an item from the designated category. We then focus on the cases where each agent is either optimistic or pessimistic, and for any sequential allocation, we characterize a tight lower bound on the rank of the allocated bundle for each agent.