2018/04/25 by Siddharth Barman, Barman, Siddharth, Arpita Biswas +1 · 6 citations
Computer Science · Decision Sciences · Economics, Econometrics and Finance · #Artificial Intelligence (cs.AI) #Auction Theory and Applications #Complexity and Algorithms in Graphs #Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences #Game Theory and Voting Systems
paper · pdf · doi:10.48550/arxiv.1804.09521
openalex publication_date 2018/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the problem of fairly allocating indivisible goods, among agents, under cardinality constraints and additive valuations. In this setting, we are given a partition of the entire set of goods---i.e., the goods are categorized---and a limit is specified on the number of goods that can be allocated from each category to any agent. The objective here is to find a fair allocation in which the subset of goods assigned to any agent satisfies the given cardinality constraints. This problem naturally captures a number of resource-allocation applications, and is a generalization of the well-studied (unconstrained) fair division problem. The two central notions of fairness, in the context of fair division of indivisible goods, are envy freeness up to one good (EF1) and the (approximate) maximin share guarantee (MMS). We show that the existence and algorithmic guarantees established for these solution concepts in the unconstrained setting can essentially be achieved under cardinality constraints. Specifically, we develop efficient algorithms which compute EF1 and approximately MMS allocations in the constrained setting. Furthermore, focusing on the case wherein all the agents have the same additive valuation, we establish that EF1 allocations exist and can be computed efficiently even under laminar matroid constraints.