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Axiomatizations of the proportional Shapley value

Besner, Manfred (2017): Axiomatizations of the proportional Shapley value. Published in: Theory and Decision , Vol. 86, No. 2 (31 January 2019): pp. 161-183.

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Abstract

We provide new axiomatic characterizations of the proportional Shapley value, a weighted TU-value with the worths of the singletons as weights. The presented characterizations are proportional counterparts to the famous characterizations of the Shapley value by Shapley (1953b) and Young (1985a). We introduce two new axioms, called proportionality and player splitting respectively. Each of them makes a main difference between the proportional Shapley value and the Shapley value. If the stand-alone worths are plausible weights, the proportional Shapley value is a convincing alternative to the Shapley value, for example in cost allocation. Especially the player splitting property, which states that the players’ payoffs do not change if another player splits into two new players who have the same impact to the game as the original player, justifies the use of the proportional Shapley value in many economic situations.

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