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Efficiency and Collusion Neutrality of Solutions for Cooperative TU-Games


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  • Rene van den Brink

    (VU University Amsterdam)


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.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 09-065/1.

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Date of creation: 22 Jul 2009
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Handle: RePEc:dgr:uvatin:20090065

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Keywords: Efficiency; Collusion neutrality; Shapley value; Banzhaf value; Equal division solution; Impossibility;

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Cited by:
  1. Aymeric Lardon, 2009. "The gamma-core in Cournot oligopoly TU-games with capacity constraints," Post-Print halshs-00544042, HAL.
  2. Aymeric Lardon, 2012. "The γ-core in Cournot oligopoly TU-games with capacity constraints," Theory and Decision, Springer, vol. 72(3), pages 387-411, March.


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