Concept

Excess

How much better a coalition could do alone than the division on offer gives it. Sorting every coalition's excesses and minimising the list in dictionary order picks exactly one division, whether or not any division satisfies all of them.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

Also named here as nucleolus — the same set of essays touches all of them, so they are one junction rather than several.

The quietest loudest complaint in any two of three decide. The triangle of all splits of what a three-player group is worth, with the split minimising the largest excess marked, the average split beside it, and the loudest complaint named.

The objection nobody can make louder

When no split of the winnings survives every group's objection, the core is empty and the question changes — which split makes the loudest objection as quiet as it can be? Sorting the complaints and minimising them in dictionary order picks exactly one split, always, whether or not the core exists.

applied · The core

The splits of any two of three decide that nobody can out-argue. The triangle of all splits of a joint gain, with the splits marked at which every player's loudest complaint against every other is matched by an equally loud complaint back.

An objection one player makes to another

The core lets a coalition object to everybody at once. Narrow it to one player objecting to one other, require every such objection to be met by an equally loud one coming back, and exactly one split survives — with no dictionary order anywhere in the argument.

applied · The core

Named alongside it

The objects these essays reach for when they reach for this one.

Coalition Core Imputation Nucleolus Balancedness Exhaustive search Fairness Lexicographic order Shapley value Stability

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