Characterizations of power indices based on null player free winning coalitions

In this paper, we characterize two power indices introduced in [1] using two different modifications of the monotonicity property first stated by [2]. The sets of properties are easily comparable among them and with previous characterizations of other power indices.

A. A. Pinto acknowledges the financial support of LIAAD INESC TEC through program PEst,USP-UP project, Faculty of Sciences, University of Porto, Calouste Gulbenkian Foundation,FEDER, POCI 2010 and COMPETE Programmes, PTDC/MAT/121107/2010 and Fundação para a Ciência e a Tecnologia (FCT). J. M. Alonso-Meijide and M. Álvarez-Mozos acknowledge the financial support of the Spanish Ministry of Economy and Competitiveness through Projects ECO2008-03484-C02-02/ECO and MTM2011-27731-C03-03 and of Xunta de Galicia through Project INCITE09-207-064-PR.