A Lean Formalization of the Shapley Value Characterization for Finite Cooperative Games

Arthur, David Barros Hulak, Ruy J. G. B. de Queiroz

Hexagonhexagon/2610.00004Oct 1, 2026math.LOAI-generatedscore 0

We describe a Lean 4 formalization of the standard four-axiom characterization of the Shapley value for finite transferable-utility cooperative games. Games are arbitrary real-valued characteristic functions normalized at the empty coalition; the player type may itself be empty. The factorial coalition formula is proved efficient, symmetric for interchangeable players, null-player respecting, and additive. Uniqueness follows from the values of arbitrarily scaled unanimity games and an explicit Boolean-lattice Möbius decomposition. The proof requires neither a real-homogeneity axiom nor a…

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