Efficiency and Collusion Neutrality of Solutions for Cooperative TU-Games

Arbeitspapier

Three well-known solutions for cooperative TU-games are the Shapley value, the Banzhaf value and the equal division solution. In the literature various axiomatizations of these solutions can be found. Axiomatizations of the Shapley value often use efficiency which is not satisfied by the Banzhaf value. On the other hand, the Banzhaf value satisfies collusion neutrality which is not satisfied by the Shapley value. Both properties seem desirable. However, neither the Shapley value nor the Banzhaf value satisfy both. The equal division solution does satisfy both axioms and, moreover, together with symmetry these axioms characterize the equal division solution. Further, we show that there is no solution that satisfies efficiency, collusion neutrality and the null player property. Finally, we show that a solution satisfies efficiency, collusion neutrality and linearity if and only if there exist exogenous weights for the players such that in any game the worth of the 'grand coalition' is distributed proportional to these weights.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: Tinbergen Institute Discussion Paper ; No. 09-065/1

Classification and Topics

• Classification: Wirtschaft ; Cooperative Games
• Subject: Efficiency ; Collusion neutrality ; Shapley value ; Banzhaf value ; Equal division solution ; Impossibility ; Transferable Utility Games ; Shapley-Wert ; Verteilungsgerechtigkeit ; Kooperatives Spiel ; Theorie

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): van den Brink, Rene
• Event: Veröffentlichung
• (who): Tinbergen Institute
• (where): Amsterdam and Rotterdam
• (when): 2009

Further information

• Handle: http://hdl.handle.net/10419/86953
• Last update: 10.03.2025, 11:43 AM CET