Two new power indices based on winning coalitions

Deegan and Packel (1979) and Holler (1982) proposed two power indices for simple games: the Deegan–Packel index and the Public Good Index. In the definition of these indices, only minimal winning coalitions are taken into account. Using similar arguments, we define two new power indices. These new indices are defined taking into account only those winning coalitions that do not contain null players. The results obtained with the different power indices are compared by means of two real-world examples taken from the political field.

A fractional perspective to financial indices

The application of mathematical methods and computer algorithms in the analysis of economic and financial data series aims to give empirical descriptions of the hidden relations between many complex or unknown variables and systems. This strategy overcomes the requirement for building models based on a set of ‘fundamental laws’, which is the paradigm for studying phenomena usual in physics and engineering. In spite of this shortcut, the fact is that financial series demonstrate to be hard to tackle, involving complex memory effects and a apparently chaotic behaviour. Several measures for describing these objects were adopted by market agents, but, due to their simplicity, they are not capable to cope with the diversity and complexity embedded in the data. Therefore, it is important to propose new measures that, on one hand, are highly interpretable by standard personal but, on the other hand, are capable of capturing a significant part of the dynamical effects.