Balancedness
Named by 3 essays across one field — each of them below, with the objects they name alongside it.
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.
Five weighings and the question is closed
Searching the triangle of splits can only ever fail to find a stable one, which is not the same as there being none. Weighing five families of coalitions against the whole settles the question outright — and the family that fails is the proof that nothing survives.
A core is a rare thing to find at random
A game has a core when the whole can be shared so that no group would do better on its own, and Bondareva and Shapley turned that into a finite list of checks. For three players there are five checks; for four, forty-one; for five, 1,291. Draw the coalitions' values at random and the list wins: a third of three-player games fail, nineteen four-player games in twenty, and not one five-player game in two thousand passes. The cores that theorems promise come from structure, and structure is exactly what a random game lacks.
Named alongside it
The objects these essays reach for when they reach for this one.
CoalitionCoreDualityExhaustive searchImputationLinear programConvexityCooperative gameExcessExistence proofLexicographic orderMonte Carlo