An axiomatic characterization of the Owen‐Shapley spatial power index

An axiomatic characterization of the Owen‐Shapley spatial power index

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Article ID: iaor20171822
Volume: 46
Issue: 2
Start Page Number: 525
End Page Number: 545
Publication Date: May 2017
Journal: International Journal of Game Theory
Authors: ,
Keywords: simulation
Abstract:

We present an axiomatic characterization of the Owen–Shapley spatial power index for the case where issues are elements of two‐dimensional space. This characterization employs a version of the transfer condition, which enables us to unravel a spatial game into spatial games connected to unanimity games. The other axioms include two conditions concerned particularly with the spatial positions of the players, besides spatial versions of anonymity and dummy. The last condition says that dummy players can be left out in a specific way without changing the power of the other players. We show that this condition can be weakened to requiring dummies to have zero power if we add a condition of positional continuity. We also show that the axioms in our characterization(s) are logically independent.

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