Efficient Nearly-Fair Division with Capacity Constraints

Research output: Contribution to journalConference articlepeer-review


We consider the problem of fairly and efficiently allocating indivisible items (goods or bads) under capacity constraints. In this setting, we are given a set of categorized items. Each category has a capacity constraint (the same for all agents), that is an upper bound on the number of items an agent can receive from each category. Our main result is a polynomial-time algorithm that solves the problem for two agents with additive utilities over the items. When each category contains items that are all goods (positively evaluated) or all chores (negatively evaluated) for each of the agents, our algorithm finds a feasible allocation of the items, which is both Pareto-optimal and envy-free up to one item. In the general case, when each item can be a good or a chore arbitrarily, our algorithm finds an allocation that is Pareto-optimal and envy-free up to one good and one chore. Full version is available at arXiv [36].

Original languageEnglish
Pages (from-to)206-214
Number of pages9
JournalProceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS
StatePublished - 2023
Event22nd International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2023 - London, United Kingdom
Duration: 29 May 20232 Jun 2023


  • Capacity constraints
  • Fair division
  • Indivisible items
  • Mixed manna

All Science Journal Classification (ASJC) codes

  • Artificial Intelligence
  • Software
  • Control and Systems Engineering


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