scholarly journals Luxembourg in the Early Days of the EEC: Null Player or Not?

Games ◽  
2018 ◽  
Vol 9 (2) ◽  
pp. 29 ◽  
Author(s):  
Alexander Mayer
Keyword(s):  
Null Player

Reformulation of Some Indices Using Null Player Free Winning Coalitions

2021 ◽  
pp. 108-115
Author(s):  
Izabella Stach ◽  
Cesarino Bertini
Keyword(s):  
Null Player

scholarly journals Characterizations of power indices based on null player free winning coalitions

Optimization ◽  
2013 ◽  
pp. 1-12 ◽  
Author(s):  
M. Alvarez-Mozos ◽  
F. Ferreira ◽  
J.M. Alonso-Meijide ◽  
A.A. Pinto
Keyword(s):  
Power Indices ◽  
Null Player

NULL PLAYERS OUT? LINEAR VALUES FOR GAMES WITH VARIABLE SUPPORTS

1999 ◽  
Vol 01 (03n04) ◽  
pp. 301-314 ◽  
Author(s):  
JEAN J. M. DERKS ◽  
HANS H. HALLER
Keyword(s):  
Cooperative Games ◽  
Symmetry Property ◽  
Sufficient Conditions ◽  
Function Form ◽  
Individual Values ◽  
Null Player ◽  
Main Emphasis ◽  
Weak Symmetry ◽  
Necessary And Sufficient ◽  
Characteristic Function Form

The paper studies the consequences of the Null Player Out (NPO) property for single-valued solutions on the class of cooperative games in characteristic function form. We allow for variable player populations (supports or carriers). A solution satisfies the NPO property, if elimination of a null player does not affect the payoffs of the other players. Our main emphasis lies on individual values. For linear values satisfying the null player property and a weak symmetry property, necessary and sufficient conditions for the NPO property are derived.

Two-step CS-value without null player and null coalition axioms

2015 ◽  
Vol 9 ◽  
pp. 6817-6825
Author(s):  
Alexandra B. Zinchenko
Keyword(s):  
Null Player

scholarly journals OUTSIDE OPTIONS IN PROBABILISTIC COALITION SITUATIONS

2011 ◽  
Vol 13 (04) ◽  
pp. 417-442 ◽  
Author(s):  
JULIA BELAU
Keyword(s):  
Coalition Structure ◽  
Axiomatic Characterization ◽  
Tu Games ◽  
Outside Option ◽  
Null Player ◽  
Coalition Structures ◽  
Outside Options ◽  
Probabilistic Setting ◽  
Probabilistic Version

In this paper, we introduce an extension of (TU) games with a coalition structure. Taking a situation where all coalitions are already established is not reasonable in order to forecast the reality; there is not only one possible coalition, there are several. We consider situations where coalitions are not established yet and take into account the likelihood of each possible coalition. This leads to a generalized, probabilistic setting for coalition structures. Probabilistic versions of known axioms as efficiency, symmetry or the null player axiom are introduced as well as new probabilistic axioms, the probabilistic influence axioms. The focus is on a generalization of the outside-option-sensitive χ-value in the new setting and an axiomatic characterization of it. The problematic of the impossibility of a direct axiomatization via deterministic pendants is discussed: As an example for a direct characterization we introduce and characterize a probabilistic version of the outside-option-insensitive pendant of the χ-value, the component restricted Shapley value. As another example for an outside-option-sensitive value without direct characterization we introduce a probabilistic version of the Owen value and show that a direct characterization is not possible; we link this to the problem of component decomposability.

scholarly journals Reformulation of Public Help Index θ Using Null Player Free Winning Coalitions

2021 ◽  
Author(s):  
Izabella Stach
Keyword(s):  
Simple Game ◽  
Computational Cost ◽  
Space Complexity ◽  
The Public ◽  
Null Player

AbstractThis paper proposes a new representation for the Public Help Index θ (briefly, PHI θ). Based on winning coalitions, the PHI θ index was introduced by Bertini et al. in (2008). The goal of this article is to reformulate the PHI θ index using null player free winning coalitions. The set of these coalitions unequivocally defines a simple game. Expressing the PHI θ index by the winning coalitions that do not contain null players allows us in a transparent way to show the parts of the power assigned to null and non-null players in a simple game. Moreover, this new representation may imply a reduction of computational cost (in the sense of space complexity) in algorithms to compute the PHI θ index if at least one of the players is a null player. We also discuss some relationships among the Holler index, the PHI θ index, and the gnp index (based on null player free winning coalitions) proposed by Álvarez-Mozos et al. in (2015).

MEASURING THE POWER OF PARTIES WITHIN GOVERNMENT COALITIONS

2007 ◽  
Vol 09 (02) ◽  
pp. 307-322 ◽  
Author(s):  
HARALD WIESE
Keyword(s):  
Cooperative Game ◽  
Power Index ◽  
Coalition Structure ◽  
Weighted Majority ◽  
Null Player ◽  
Outside Options ◽  
Weighted Majority Games ◽  
Majority Games

The paper presents a coalition-structure value that is meant to capture outside options of players in a cooperative game. It deviates from the Aumann-Drèze value by violating the null-player axiom. We use this value as a power index and apply it to weighted majority games.

scholarly journals An Axiomatization for Two Power Indices for (3,2)-Simple Games

2019 ◽  
Vol 21 (01) ◽  
pp. 1940001 ◽  
Author(s):  
Giulia Bernardi ◽  
Josep Freixas
Keyword(s):  
Power Index ◽  
Power Indices ◽  
Simple Games ◽  
Banzhaf Index ◽  
Null Player

The aim of this work is to give a characterization of the Shapley–Shubik and the Banzhaf power indices for (3,2)-simple games. We generalize to the set of (3,2)-simple games the classical axioms for power indices on simple games: transfer, anonymity, null player property and efficiency. However, these four axioms are not enough to uniquely characterize the Shapley–Shubik index for (3,2)-simple games. Thus, we introduce a new axiom to prove the uniqueness of the extension of the Shapley–Shubik power index in this context. Moreover, we provide an analogous characterization for the Banzhaf index for (3,2)-simple games, generalizing the four axioms for simple games and adding another property.

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