We study the congested assignment problem as introduced by Bogomolnaia and Moulin (2023). We show that deciding whether a competitive assignment exists can be done in polynomial time, while deciding whether an envy-free assignment exists is NP-complete.

翻译：我们研究了Bogomolnaia和Moulin（2023）提出的拥堵分配问题。我们证明了判断是否存在竞争性分配可以在多项式时间内完成，而判断是否存在无嫉妒分配则是NP完全的。