Three-valued simple games

M Musegaas,M Quant,P E M Borm

doi:10.1007/s11238-017-9630-z

M Musegaas, M Quant + Show 1 more

Open Access

https://doi.org/10.1007/s11238-017-9630-z

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Abstract

In this paper we study three-valued simple games as a natural extension of simple games. We analyze to which extent well-known results on the core and the Shapley value for simple games can be extended to this new setting. To describe the core of a three-valued simple game we introduce (primary and secondary) vital players, in analogy to veto players for simple games. Moreover, it is seen that the transfer property of Dubey (1975) can still be used to characterize the Shapley value for three-valued simple games. We illustrate three-valued simple games and the corresponding Shapley value in a parliamentary bicameral system.

Highlights

In this paper we analyze a class of transferable utility games, called three-valued simple games
We study how the results for simple games can be extended to three-valued simple games
We extend the notion of veto players in simple games, to the notion of vital players, primary vital players and secondary vital pairs in three-valued simple games

Summary

Introduction

In this paper we analyze a class of transferable utility games, called three-valued simple games. This paper formally defines the class of three-valued simple games and focuses on analyzing the core and the Shapley value of these games. Dubey (1975) characterized the Shapley value on the class of simple games. The essence of this characterization is the transfer property. We prove that the combination of the axioms of efficiency, symmetry, the dummy property, the transfer property and unanimity level efficiency fully determines the Shapley value for a three-valued simple game.

Simple and three-valued simple games

The core of three-valued simple games

The Shapley value for three-valued simple games