X Allocating Indivisible Items in Categorized Domains

To overcome the communicational and computational barriers in allocation problems of indivisible items, we propose a novel and general class of allocation problems called categorized domain allocation problems (CDAPs), where the indivisible items are partitioned into multiple categories and we must allocate the items to the agents without monetary transfer, such that each agent gets at least one item from each category. We focus on the design and analysis of allocation mechanisms for basic CDAPs, where the number of items in each category is exactly the same as the number of agents. We start with serial dictatorships and characterize them by a minimal set of three properties: strategy-proofness, non-bossiness, and categorywise neutrality. Then, we design and analyze a natural extension of serial dictatorships called categorical sequential allocation mechanisms, which allocate the items in multiple rounds so that in each round, the active agent chooses an item from the designated category. We characterize the worst-case ordinal efficiency of categorical sequential allocation mechanisms for optimistic and pessimistic agents, and use computer simulations to study the expected efficiency of these mechanisms.