Cooperative Game Theory & Power Indices

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Abstractions about allocating value and power in games, covering cooperative-game solution concepts (Shapley value, imputations, Mertens-stable equilibrium), voting-power measures (Banzhaf and Shapley-Shubik indices), and strategic paradoxes or mechanisms like the chainstore and lottery paradoxes and truthful cake-cutting.

12 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.
• Chainstore paradox — The conflict between backward-induction accommodation and reputation-based deterrence in a finitely repeated entry game with sequential challengers.
• Gittins index — Assign each state of an eligible discounted Markov reward arm the greatest reward rate attainable before an adapted stopping time, enabling an optimal classical bandit policy by selecting the arm with largest current index.
• 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.
• Lottery mathematics — The combinatorial and probabilistic analysis of lottery drawings, prize tiers, expected returns and apparent coincidences under declared game rules.
• Lottery paradox — The inconsistency between accepting each highly probable claim that an individual lottery ticket will lose and accepting the certain claim that some ticket will win.
• Mertens-stable equilibrium — A robust set-valued refinement of Nash equilibrium requiring strategically coherent equilibrium components to persist under admissible perturbations and satisfy invariance and rationality properties.
• Nash equilibrium computation — The computational problem of finding an exact or approximate Nash equilibrium from a represented game and reporting a strategy profile with bounded unilateral deviation gain.
• 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.
• Strategy-stealing argument — A nonconstructive game-theoretic proof that a second-player winning strategy would let the first player make a harmless opening move and then adopt that strategy, producing a contradiction.
• 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.