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Player splitting, players merging, the Shapley set value and the Harsanyi set value

Besner, Manfred (2018): Player splitting, players merging, the Shapley set value and the Harsanyi set value.

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Abstract

We discuss a value, proposed in the context of cost allocation by Shapley (1981) and Dehez (2011) and in general by Radzik (2012). This value, we call it Shapley set value, covers the weighted Shapley values all at once. It is defined on weighted TU-games in the form of two constituent parts, a weight system and a classical TU-game, where the weights and the coalition function may vary at the same time. In addition, similar to the Shapley set value, we introduce the Harsanyi set value. It captures all TU-values from the Harsanyi set, called Harsanyi payoffs. A player splitting and a players merging property enable new axiomatizations. Examples recommend both solution concepts for profit distribution and cost allocation.

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