Computational complexity of necessary envy-freeness

Haris Aziz, Ildikó Schlotter, Toby Walsh

Abstract: Highlights•Envy-free allocation of indivisible items to a few agents is computationally hard.•Finding a necessarily envy-free allocation is NP-hard already for 3 agents.•For any n≥3<math><mrow is="true"><mi is="true">n</mi><mo linebreak="goodbreak" linebreakstyle="after" is="true">≥</mo><mn is="true">3</mn></mrow></math>, finding a necessarily envy-free allocation for n<math><mi is="true">n</mi></math> agents is NP-hard.