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The Shapley Value, Proper Shapley Value, and Sharing Rules for Cooperative Ventures

Rene (J.R.) van den Brink (), Rene Levinsky () and Miroslav Zeleny ()
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Rene (J.R.) van den Brink: VU University, Amsterdam
Rene Levinsky: Economics Institute, Praha
Miroslav Zeleny: Charles University, Praha

No 18-089/II, Tinbergen Institute Discussion Papers from Tinbergen Institute

Abstract: Moulin (1987) studies the equal and proportional sharing rule for a special class of cooperative games that he calls joint venture games. Proportionality is an important principle in allocation problems. Besides some special cases, it is not obvious how proportionality should be applied in cooperative TU-games. Such special cases, where proportionality is obvious, are inessential games and cooperative joint venture games. In this paper, we discuss an explicit axiom that shows that proper Shapley values can be seen as an appropriate way to express proportionality in value allocation in cooperative TU-games. We characterize positive proper Shapley values by affine invariance and an axiom that requires proportional allocation according to the individual singleton worths in generalized joint venture games. As a counterpart, we show that affine invariance and an axiom that requires equal allocation of the surplus in generalized joint venture games, characterize the positive part of the Shapley value among the single-valued solutions.

Keywords: Equity principle; Cooperative venture game; Shapley value; proper Shapley value (search for similar items in EconPapers)
JEL-codes: C71 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-des and nep-gth
Date: 2018-11-16
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