Fair Division & Cooperative Power

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Abstractions about cooperative-game values, voting power, imputations, Pareto efficiency, envy-free allocation, and truthful division protocols.

7 abstractions in this family — domain-specific abstractions that sit near one another in structural-signature space (k-means over structural-signature embeddings). Each is shown with its short description.

• Banzhaf power index — A voting-power measure based on how often a voter is critical in winning coalitions, normalized either across that voter's possible swings or across all voters' swings.
• Efficient envy-free division — A resource allocation that is both Pareto efficient and envy-free, so no feasible change benefits someone without harming another and no agent prefers another’s bundle to their own.
• Fractional Pareto efficiency — A discrete allocation is fractionally Pareto-efficient when no feasible allocation, including fractional ones, can make every agent at least as well off and one strictly better off.
• Imputation (Game Theory) — A payoff allocation in a transferable-utility cooperative game that distributes the grand coalition's entire worth while giving every player at least its stand-alone coalition value.
• Shapley value — The unique cooperative-game allocation that assigns each player their average marginal contribution over all coalition-entry orders under efficiency, symmetry, dummy and additivity axioms.
• Shapley–Shubik power index — A voter’s a priori power measured as the probability of being pivotal over all orderings in a monotone simple voting game.
• Truthful cake-cutting — The design of fair-division mechanisms for a heterogeneous divisible resource in which truthful reporting of valuations is an optimal strategy for participants.