Power measures derived from the sequential query process

TL;DR

This paper introduces a new family of power measures for simple and TU-games based on sequential query processes, extending existing indices like Shapley-Shubik and including a novel measure closely related to the Shapley value.

Contribution

It derives a uniform family of power measures from sequential query models, highlighting a new measure that is different from but related to the Shapley value, and extends to TU-games.

Findings

Introduces a new power measure related to the Shapley value.

Extends the measures to TU-games, including all weighted semivalues.

Provides illustrative calculations on standard examples.

Abstract

We study a basic sequential model for the discovery of winning coalitions in a simple game, well known from its use in defining the Shapley-Shubik power index. We derive in a uniform way a family of measures of collective and individual power in simple games, and show that, as for the Shapley-Shubik index, they extend naturally to measures for TU-games. In particular, the individual measures include all weighted semivalues. We single out the simplest measure in our family for more investigation, as it is new to the literature as far as we know. Although it is very different from the Shapley value, it is closely related in several ways, and is the natural analogue of the Shapley value under a nonstandard, but natural, definition of simple game. We illustrate this new measure by calculating its values on some standard examples.