Decomposition of the space of TU-games, Strong Transfer Invariance and the Banzhaf value

Sylvain Béal, Eric Rémila and Philippe Solal

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Abstract: We provide a new and concise characterization of the Banzhaf value on the (linear) space of all TU-games on a fixed player set by means of two transparent axioms. The first one is the well-known Dummy player axiom. The second axiom, called Strong transfer invariance, indicates that a player's payoff is invariant to a transfer of worth between two coalitions he or she belongs to. To prove this result we derive direct-sum decompositions of the space of all TU-games. We show that, for each player, the space of all TU-games is the direct sum of the subspace of TU-games where this player is dummy and the subspace spanned by the TU-games used to construct the transfers of worth. This decomposition method has several advantages listed as concluding remarks.

Keywords: Direct-sum decomposition; Banzhaf value; Dummy player axiom; Strong Transfer invariance (search for similar items in EconPapers)
Date: 2014-11-01
Note: View the original document on HAL open archive server: https://hal.science/hal-01377929v1
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Related works:
Working Paper: Decomposition of the space of TU-games, Strong Transfer Invariance and the Banzhaf value (2015)
Working Paper: Decomposition of the space of TU-games, Strong Transfer Invariance and the Banzhaf value (2014)
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