scholarly journals Minimal winning coalitions and orders of criticality

2021 ◽  
Author(s):  
Michele Aleandri ◽  
Marco Dall’Aglio ◽  
Vito Fragnelli ◽  
Stefano Moretti
Keyword(s):  
Simple Game ◽  
Simple Games ◽  
Hitting Sets ◽  
The Family ◽  
Minimal Winning Coalitions ◽  
Minimal Blocking

AbstractIn this paper, we analyze the order of criticality in simple games, under the light of minimal winning coalitions. The order of criticality of a player in a simple game is based on the minimal number of other players that have to leave so that the player in question becomes pivotal. We show that this definition can be formulated referring to the cardinality of the minimal blocking coalitions or minimal hitting sets for the family of minimal winning coalitions; moreover, the blocking coalitions are related to the winning coalitions of the dual game. Finally, we propose to rank all the players lexicographically accounting the number of coalitions for which they are critical of each order, and we characterize this ranking using four independent axioms.

scholarly journals Bounds for Owen's Multilinear Extension

2007 ◽  
Vol 44 (4) ◽  
pp. 852-864 ◽  
Author(s):  
Josep Freixas
Keyword(s):  
Game Theory ◽  
Simple Game ◽  
Practical Interest ◽  
Simple Games ◽  
Theoretical Interest ◽  
Complex Component ◽  
Multilinear Extension ◽  
Voting System ◽  
Minimal Winning Coalitions ◽  
Minimal Blocking

Owen's multilinear extension (MLE) of a game is a very important tool in game theory and particularly in the field of simple games. Among other applications it serves to efficiently compute several solution concepts. In this paper we provide bounds for the MLE. Apart from its self-contained theoretical interest, the bounds offer the means in voting system studies of approximating the probability that a proposal is approved in a particular simple game having a complex component arrangement. The practical interest of the bounds is that they can be useful for simple games having a tedious MLE to evaluate exactly, but whose minimal winning coalitions and minimal blocking coalitions can be determined by inspection. Such simple games are quite numerous.

scholarly journals Bounds for Owen's Multilinear Extension

2007 ◽  
Vol 44 (04) ◽  
pp. 852-864 ◽  
Author(s):  
Josep Freixas
Keyword(s):  
Game Theory ◽  
Simple Game ◽  
Practical Interest ◽  
Simple Games ◽  
Theoretical Interest ◽  
Complex Component ◽  
Multilinear Extension ◽  
Voting System ◽  
Minimal Winning Coalitions ◽  
Minimal Blocking

Owen's multilinear extension (MLE) of a game is a very important tool in game theory and particularly in the field of simple games. Among other applications it serves to efficiently compute several solution concepts. In this paper we provide bounds for the MLE. Apart from its self-contained theoretical interest, the bounds offer the means in voting system studies of approximating the probability that a proposal is approved in a particular simple game having a complex component arrangement. The practical interest of the bounds is that they can be useful for simple games having a tedious MLE to evaluate exactly, but whose minimal winning coalitions and minimal blocking coalitions can be determined by inspection. Such simple games are quite numerous.

NEW APPORTIONMENT METHODS USING SIMPLE GAMES

2010 ◽  
Vol 12 (03) ◽  
pp. 211-222
Author(s):  
EVAN SHELLSHEAR
Keyword(s):  
Simple Game ◽  
Simple Games ◽  
New Methods ◽  
Apportionment Methods

This paper investigates the suitability of new apportionment methods based on the idea of preserving the coalition function of the simple game generated by the populations of the states of some country. The new methods fill a gap in the literature concerning apportionment methods based on winning coalitions. The main results in this paper show that the new apportionment methods do not satisfy desirable properties such as house monotonicity, quota, etc.

A Note on the Owen Value for Glove Games

2015 ◽  
Vol 17 (04) ◽  
pp. 1550014 ◽  
Author(s):  
Julia Belau
Keyword(s):  
Shapley Value ◽  
Simple Game ◽  
Computational Effort ◽  
Computationally Efficient ◽  
Owen Value ◽  
Allocation Rules ◽  
The Shapley Value ◽  
Minimal Winning Coalitions

A well-known and simple game to model markets is the glove game where worth is produced by building matching pairs. For glove games, different concepts, like the Shapley value, the component restricted Shapley value or the Owen value, yield different distributions of worth. While the Shapley value does not distinguish between productive and unproductive agents in the market and the component restricted Shapley value does not consider imbalancedness of the market, the Owen value accounts for both. As computational effort for Shapley-based allocation rules is generally high, this note provides a computationally efficient formula for the Owen value (and the component restricted Shapley value) for glove games in case of minimal winning coalitions. A comparison of the efficient formulas highlights the above-mentioned differences.

scholarly journals Neuropsychologist’s Experience with the DIRFloortime Concept. A Clinical Case Report

2019 ◽  
Vol 17 (2) ◽  
pp. 87-96
Author(s):  
S.A. Shishkina
Keyword(s):  
Case Report ◽  
Emotional Development ◽  
Clinical Case ◽  
Family Members ◽  
Individual Characteristics ◽  
Simple Games ◽  
Joint Work ◽  
The Family ◽  
Speech Therapist

The article analyzes the experience of the joint work of a speech therapist and a neuropsychologist using the DIRFloortime concept on a clinical case of a boy L., 3.5 years of age. The following tasks were solved during the sessions: the child’s advancement along the first stages of functional emotional development, taking into account his individual characteristics; work with the family: establishing a partnership, teaching the family members the basics of the DIRFloortime approach. As a result of the sessions, the child’s understanding of speech and implementation of instructions have significantly improved; he started using meaningful words and phrases for communication; his emotional and non-verbal repertoire expanded, the boy learned to play simple games with rules with an adult.

scholarly journals An issue based power index

2020 ◽  
Author(s):  
Qianqian Kong ◽  
Hans Peters
Keyword(s):  
Linear Order ◽  
Power Index ◽  
Simple Game ◽  
Power Indices ◽  
Weighted Sum ◽  
Simple Games ◽  
Linear Orders ◽  
Transfer Property ◽  
Power Change ◽  
Equal Power

Abstract An issue game is a combination of a monotonic simple game and an issue profile. An issue profile is a profile of linear orders on the player set, one for each issue within the set of issues: such a linear order is interpreted as the order in which the players will support the issue under consideration. A power index assigns to each player in an issue game a nonnegative number, where these numbers sum up to one. We consider a class of power indices, characterized by weight vectors on the set of issues. A power index in this class assigns to each player the weighted sum of the issues for which that player is pivotal. A player is pivotal for an issue if that player is a pivotal player in the coalition consisting of all players preceding that player in the linear order associated with that issue. We present several axiomatic characterizations of this class of power indices. The first characterization is based on two axioms: one says how power depends on the issues under consideration (Issue Dependence), and the other one concerns the consequences, for power, of splitting players into several new players (no advantageous splitting). The second characterization uses a stronger version of Issue Dependence, and an axiom about symmetric players (Invariance with respect to Symmetric Players). The third characterization is based on a variation on the transfer property for values of simple games (Equal Power Change), besides Invariance with respect to Symmetric Players and another version of Issue Dependence. Finally, we discuss how an issue profile may arise from preferences of players about issues.

scholarly journals Power Indices and Minimal Winning Coalitions for Simple Games in Partition Function Form

2017 ◽  
Vol 26 (6) ◽  
pp. 1231-1245 ◽  
Author(s):  
J. M. Alonso-Meijide ◽  
M. Álvarez-Mozos ◽  
M. G. Fiestras-Janeiro
Keyword(s):  
Partition Function ◽  
Power Indices ◽  
Simple Games ◽  
Function Form ◽  
Partition Function Form ◽  
Minimal Winning Coalitions

scholarly journals Simple Games of Information Transmission

2012 ◽  
Vol 34 (2) ◽  
Author(s):  
Bernd Lahno
Keyword(s):  
Information Transmission ◽  
Simple Game ◽  
Strategic Analysis ◽  
Direct Impact ◽  
Simple Games ◽  
Game Theoretic ◽  
The Will

AbstractCommunication is an inherently strategic matter. This paper introduces simple game theoretic models of information transmission to identify different forms of uncertainty which may pose a problem of trust in testimony. Strategic analysis suggests discriminating between trust in integrity, trust in competence, trust in (the will to invest) effort and trust in honesty. Whereas uncertainty about the sender's honesty or integrity may directly influence a rational receiver's readiness to rely on sender's statements, neither uncertainty about the competence of a sender nor uncertainty about his willingness to invest effort has any direct impact on rational reliance on its own. In this regard, trust in honesty and trust in integrity appear to be more basic than trust in competence or effort.

SEMIVALUES AND VOTING POWER

2003 ◽  
Vol 05 (01) ◽  
pp. 41-61 ◽  
Author(s):  
ANNICK LARUELLE ◽  
FEDERICO VALENCIANO
Keyword(s):  
Power Indices ◽  
Simple Games ◽  
Voting Power ◽  
The Family ◽  
Voting Procedures

In this paper we revise the axiomatic foundations and meaning of semivalues as measures of power on the domain of simple games, when these are interpreted as models of voting procedures. In this context we characterize the family of preferences on roles in voting procedures they represent, and each of them in particular. To this end we first characterize the family of semivalues and each of them in particular up to the choice of a zero and a unit of scale. As a result a reinterpretation of semivalues as a class of power indices is proposed and critically discussed.

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