Coalitional substitution of players and the proportional Shapley value

Besner, Manfred (2025): Coalitional substitution of players and the proportional Shapley value.

Abstract

We present a new axiomatization of the proportional Shapley Value. Our study is based on three axioms: efficiency, which ensures that the total worth of the grand coalition is fully distributed among the players; the disjointly productive players property, which states that removing a player who has no cooperative interactions with another player does not affect that player's payoff; and a new axiom that makes the difference to the classical Shapley value. This axiom, the coalitional substitution of players property, involves a scenario in which a player's cooperative contribution to a coalition is replaced by that of a group of new players whose combined individual worths match that of the original player. The key point is that the payoffs to the remaining players remain unaffected.

• Item Type: MPRA Paper
• Language: English
• Keywords: Cooperative game; Proportional Shapley value; Disjointly productive players; Coalitional substitution of players; Patronage refunds
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C71 - Cooperative Games; D - Microeconomics > D6 - Welfare Economics > D60 - General

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