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

Arbeitspapier

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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: Tinbergen Institute Discussion Paper ; No. TI 2018-089/II

Classification and Topics

• Classification: Wirtschaft ; Cooperative Games
• Subject: Equity principle ; Cooperative venture game ; Shapley value ; proper Shapley value

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): van den Brink, Rene ; Levinsky, Rene ; Zeleny, Miroslav
• Event: Veröffentlichung
• (who): Tinbergen Institute
• (where): Amsterdam and Rotterdam
• (when): 2018

Further information

• Handle: http://hdl.handle.net/10419/185608
• Last update: 10.03.2025, 11:43 AM CET