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

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.

Download Full-text

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

Applied Mathematical Sciences ◽

10.12988/ams.2015.59586 ◽

2015 ◽

Vol 9 ◽

pp. 6817-6825

Author(s):

Alexandra B. Zinchenko

Keyword(s):

Null Player

Download Full-text

OUTSIDE OPTIONS IN PROBABILISTIC COALITION SITUATIONS

International Game Theory Review ◽

10.1142/s0219198911003076 ◽

2011 ◽

Vol 13 (04) ◽

pp. 417-442 ◽

Cited By ~ 5

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.

Download Full-text

MEASURING THE POWER OF PARTIES WITHIN GOVERNMENT COALITIONS

International Game Theory Review ◽

10.1142/s0219198907001412 ◽

2007 ◽

Vol 09 (02) ◽

pp. 307-322 ◽

Cited By ~ 27

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.

Download Full-text

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

International Game Theory Review ◽

10.1142/s0219198919400012 ◽

2019 ◽

Vol 21 (01) ◽

pp. 1940001 ◽

Cited By ~ 1

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.

Download Full-text

Modeling values for TU-games using generalized versions of consistency, standardness and the null player property

Mathematical Methods of Operations Research ◽

10.1007/s00186-015-0525-x ◽

2015 ◽

Vol 83 (2) ◽

pp. 179-205 ◽

Cited By ~ 8

Author(s):

Tadeusz Radzik ◽

Theo Driessen

Keyword(s):

Tu Games ◽

Null Player

Download Full-text

A CONSISTENT IMPUTATION GENERATION METHOD FOR LINGUISTIC COOPERATIVE GAMES AND ITS APPLICATION TO RISK AVERSION

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488512400041 ◽

2012 ◽

Vol 20 (supp01) ◽

pp. 49-66

Author(s):

JIAN LIN ◽

QIANG ZHANG

Keyword(s):

Game Theory ◽

Risk Aversion ◽

Shapley Value ◽

Cooperative Games ◽

Existence And Uniqueness ◽

Cooperative Game Theory ◽

Management Systems ◽

Linguistic Label ◽

Null Player ◽

Linguistic Labels

Cooperative game theory is very useful to risk aversion problems in economics and management systems. The existing methods only focus on the situation payoffs take the form of numerical values, ones take the form of linguistic labels are seldom discussed. The aim of this study is to propose the consistent imputation for cooperative games under a linguistic environment. To support risk aversion, a 2-tuple linguistic representation is employed to obtain the valid results and avoid the loss of linguistic information. This paper firstly defines some concepts for linguistic cooperative games, such as linguistic imputation, carrier, core and null player. A set of their desirable properties are also discussed. The linguistic Shapley value is then presented based on three axioms. Moreover, the existence and uniqueness of the linguistic Shapley value are discussed in detail. To adjust the linguistic imputation in accordance with the cardinality of a given original linguistic label set, an adjustment algorithm for generating consistent imputation is proposed. Finally, we give the application of linguistic imputation in solving risk aversion problems to illustrate the validity of the consistent imputation generation (CIG) method.

Download Full-text