An axiomatic characterization of the Owen-Shapley spatial power index

Hans Peters*, J.M. Zarzuelo

*Corresponding author for this work

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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.

Original languageEnglish
Pages (from-to)525-545
Number of pages21
JournalInternational Journal of Game Theory
Issue number2
Early online date2016
Publication statusPublished - May 2017


  • Simple game
  • Constellation
  • Spatial game
  • Owen-Shapley spatial power index

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