Efficiency and Collusion Neutrality of Solutions for Cooperative TU-Games
René Van den Brink
VU University Amsterdam - Department of Economics; Tinbergen Institute; Tinbergen Institute - Tinbergen Institute Amsterdam (TIA)
July 21, 2009
Tinbergen Institute Discussion Paper 09-065/1
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.
Number of Pages in PDF File: 16
Keywords: efficiency, collusion neutrality, Shapley value, Banzhaf value, equal division solution, impossibility
JEL Classification: C71working papers series
Date posted: July 25, 2009
© 2013 Social Science Electronic Publishing, Inc. All Rights Reserved.
This page was processed by apollo6 in 0.594 seconds