Envy Relay

A drag-and-drop puzzle built from a real fair-division paper.

Deligkas, Fasoulakis, Ioannidis, Mancho & Markakis (2026), “Delegated Fair Division” studies allocation through a middle layer of centers — think of a charity delegating food donations to local pantries, which then split them among their own members. Fairness has to hold at both levels at once: pantries shouldn't envy each other, and inside a pantry, nobody should envy their fellow member.

Below: 3 pantries, 2 members each, 6 donated goods. Every member secretly values each good differently — you get to see the whole grid, because you're playing the allocator, not a participant. Drag each good onto a pantry, then onto one of that pantry's two members. The checker below updates live.

This build plays the intra-fairness mode: members only compare themselves against their own pantry-mate, never against people in other pantries. Pantries are checked against each other using the paper's item-based potential value — a pantry judges another pantry's goods by imagining it split them optimally between its own two members, regardless of how that pantry actually split them.

Goods held by a pantry but not yet given to a member don't count toward any member's bundle, but they do already count toward that pantry's own valuation of what it holds — item-based potential value only cares which pantry a good belongs to.