Reduced-Form Allocations for Multiple Indivisible Objects under Constraints: A Revision

We examine the implementation of reduced-form allocation rules that assign multiple indivisible objects to many agents, with incomplete information and distributional constraints across objects and agents. To obtain implementability results, we adopt a lift-and-project approach, which enables us to and a general condition called total unimodularity, a well-recognized class of matrices with simple entries of -1, 0, or 1. This condition yields several new and general characterization results including those on hierarchies, bihierarchies, and consecutiveness. Our model and results extend and unify many well-known ones considerably, find new applications, and also apply to both ordinal and cardinal preferences.