Monotonicity implies linearity: characterizations of convex combinations of solutions to cooperative games

DOI10.1007/S00355-017-1056-6zbMath1392.91011OpenAlexW2613203402MaRDI QIDQ1704072

Yukihiko Funaki, Koji Yokote

Publication date: 8 March 2018

Published in: Social Choice and Welfare (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00355-017-1056-6

zbMATH Keywords

monotonicitycooperative gameslinear solutionconvex combinations of solutions

Mathematics Subject Classification ID

Cooperative games (91A12)

Related Items (13)

Players' dummification and the dummified egalitarian non-separable contribution value ⋮ The in-group egalitarian Owen values ⋮ Core stability of the Shapley value for cooperative games ⋮ Effects of Players’ Nullification and Equal (Surplus) Division Values ⋮ Equal loss under separatorization and egalitarian values ⋮ Similarities in axiomatizations: equal surplus division value and first-price auctions ⋮ The Egalitarian Shapley value: a generalization based on coalition sizes ⋮ The central core and the mid-central core as novel set-valued and point-valued solution concepts for transferable utility coalitional games ⋮ Redistribution to the less productive: parallel characterizations of the egalitarian Shapley and consensus values ⋮ Axiomatizations of the proportional division value ⋮ Players' nullification and the weighted (surplus) division values ⋮ Relationally equal treatment of equals and affine combinations of values for TU games ⋮ The grand surplus value and repeated cooperative cross-games with coalitional collaboration

Cites Work

• Young's axiomatization of the Shapley value: a new proof
• Duality and anti-duality in TU games applied to solutions, axioms, and axiomatizations
• Weakly monotonic solutions for cooperative games
• Axiomatizations of a class of equal surplus sharing solutions for TU-games
• Monotonic solutions of cooperative games
• Coincidence of and collinearity between game theoretic solutions
• Null players, solidarity, and the egalitarian Shapley values
• Reconciling marginalism with egalitarianism: consistency, monotonicity, and implementation of egalitarian Shapley values
• Null or nullifying players: the difference between the Shapley value and equal division solutions
• The consensus value: a new solution concept for cooperative games
• A First Course in Optimization Theory
• Monotonic redistribution of performance-based allocations: A case for proportional taxation

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