scholarly journals Harsanyi support levels solutions

2021 ◽  
Author(s):  
Manfred Besner
Keyword(s):  
Hierarchical Structure ◽  
Level Structure ◽  
Grand Coalition ◽  
Transferable Utility ◽  
Tu Games ◽  
New Class ◽  
Shapley Values ◽  
Special Case

AbstractWe introduce a new class of values for TU-games (games with transferable utility) with a level structure, called LS-games. A level structure is a hierarchical structure where each level corresponds to a partition of the player set, which becomes increasingly coarse from the trivial partition containing only singletons to the partition containing only the grand coalition. The new values, called Harsanyi support levels solutions, extend the Harsanyi solutions for LS-games. As an important subset of the class of these values, we present the class of weighted Shapley support levels values as a further result. The values from this class extend the weighted Shapley values for LS-games and contain the Shapley levels value as a special case. Axiomatizations of the studied classes are provided.

Effects of Players’ Nullification and Equal (Surplus) Division Values

2018 ◽  
Vol 20 (01) ◽  
pp. 1750029 ◽  
Author(s):  
Takumi Kongo
Keyword(s):  
The Other ◽  
Equal Division ◽  
Transferable Utility ◽  
Tu Games ◽  
Axiomatic Characterizations ◽  
The Difference ◽  
Monotonicity Axioms ◽  
Equal Surplus Division

We provide axiomatic characterizations of the solutions of transferable utility (TU) games on the fixed player set, where at least three players exist. We introduce two axioms on players’ nullification. One axiom requires that the difference between the effect of a player’s nullification on the nullified player and on the others is relatively constant if all but one players are null players. Another axiom requires that a player’s nullification affects equally all of the other players. These two axioms characterize the set of all affine combinations of the equal surplus division and equal division values, together with the two basic axioms of efficiency and null game. By replacing the first axiom on players’ nullification with appropriate monotonicity axioms, we narrow down the solutions to the set of all convex combinations of the two values, or to each of the two values.

NONEMPTY CORE-TYPE SOLUTIONS OVER BALANCED COALITIONS IN TU-GAMES

2012 ◽  
Vol 14 (03) ◽  
pp. 1250018 ◽  
Author(s):  
JUAN C. CESCO
Keyword(s):  
Equal Opportunity ◽  
Axiomatic Characterization ◽  
Individual Rationality ◽  
Transferable Utility ◽  
Tu Game ◽  
Tu Games ◽  
Additional Axiom ◽  
Game Property ◽  
Minimality Property ◽  
New Framework

In this paper we introduce two related core-type solutions for games with transferable utility (TU-games) the [Formula: see text]-core and the [Formula: see text]-core. The elements of the solutions are pairs [Formula: see text] where x, as usual, is a vector representing a distribution of utility and [Formula: see text] is a balanced family of coalitions, in the case of the [Formula: see text]-core, and a minimal balanced one, in the case of the [Formula: see text]-core, describing a plausible organization of the players to achieve the vector x. Both solutions extend the notion of classical core but, unlike it, they are always nonempty for any TU-game. For the [Formula: see text]-core, which also exhibits a certain kind of "minimality" property, we provide a nice axiomatic characterization in terms of the four axioms nonemptiness (NE), individual rationality (IR), superadditivity (SUPA) and a weak reduced game property (WRGP) (with appropriate modifications to adapt them to the new framework) used to characterize the classical core. However, an additional axiom, the axiom of equal opportunity is required. It roughly states that if [Formula: see text] belongs to the [Formula: see text]-core then, any other admissible element of the form [Formula: see text] should belong to the solution too.

scholarly journals On the ergodic distribution of oscillating queueing systems

2003 ◽  
Vol 16 (4) ◽  
pp. 311-326 ◽  
Author(s):  
Mykola Bratiychuk ◽  
Andrzej Chydzinski
Keyword(s):  
Queueing Systems ◽  
Numerical Example ◽  
New Class ◽  
Ergodic Distribution ◽  
Number Of Customers ◽  
Special Case

This paper examines a new class of queueing systems and proves a theorem on the existence of the ergodic distribution of the number of customers in such a system. An ergodic distribution is computed explicitly for the special case of a G/M−M/1 system, where the interarrival distribution does not change and both service distributions are exponential. A numerical example is also given.

scholarly journals The fates of merging supermassive black holes and a proposal for a new class of X-ray sources

2020 ◽  
Vol 498 (3) ◽  
pp. 3807-3816
Author(s):  
Charles Zivancev ◽  
Jeremiah Ostriker ◽  
Andreas H W Küpper
Keyword(s):  
Black Holes ◽  
Structure Formation ◽  
Hierarchical Structure ◽  
Dynamical Evolution ◽  
Supermassive Black Holes ◽  
Host Galaxy ◽  
X Ray ◽  
Massive Galaxies ◽  
New Class ◽  
Low Mass

ABSTRACT We perform N-body simulations on some of the most massive galaxies extracted from a cosmological simulation of hierarchical structure formation with total masses in the range 1012 M⊙ < Mtot < 3 × 1013 M⊙ from 4 ≥ z ≥ 0. After galactic mergers, we track the dynamical evolution of the infalling black holes (BHs) around their host’s central BHs (CBHs). From 11 different simulations, we find that, of the 86 infalling BHs with masses >104 M⊙, 36 merge with their host’s CBH, 13 are ejected from their host galaxy, and 37 are still orbiting at z = 0. Across all galaxies, 33 BHs are kicked to a higher orbit after close interactions with the CBH binary or multiple, after which only one of them merged with their hosts. These orbiting BHs should be detectable by their anomalous (not low-mass X-ray binary) spectra. The X-ray luminosities of the orbiting massive BHs at z = 0 are in the range $10^{28}-10^{43}\, \mathrm{erg}~\mathrm{s}^{-1}$, with a currently undetectable median value of $10^{33}\, \mathrm{erg}~\mathrm{s}^{-1}$. However, the most luminous ∼5 per cent should be detectable by existing X-ray facilities.

scholarly journals The Inverse Lomax-G Family with application to Breaking Strength Data

2020 ◽  
pp. 49-60
Author(s):  
Jamilu Yunusa Falgore ◽  
Sani Ibrahim Doguwa
Keyword(s):  
Breaking Strength ◽  
Moment Generating Function ◽  
Maximum Likelihood Estimates ◽  
Strength Data ◽  
New Class ◽  
Class A ◽  
New Family ◽  
Competing Models ◽  
Special Case ◽  
Study Application

We proposed a new class of distributions with two additional positive parameters called the Inverse Lomax-G (IL-G) class. A special case was discussed, by taking Weibull as a baseline. Different properties of the new family that hold for any type of baseline model are derived including moments, moment generating function, entropy for Renyi, entropy for Shanon, and order statistics. The performances of the maximum likelihood estimates of the parameters of the sub-model of the Inverse Lomax-G family were evaluated through a simulation study. Application of the sub-model to the Breaking strength data clearly showed its superiority overthe other competing models.

scholarly journals Global Analysis and the Periodic Character of a Class of Difference Equations

Axioms ◽  
2019 ◽  
Vol 8 (4) ◽  
pp. 131 ◽  
Author(s):  
George E. Chatzarakis ◽  
Elmetwally M. Elabbasy ◽  
Osama Moaaz ◽  
Hamida Mahjoub
Keyword(s):  
Mathematical Models ◽  
Difference Equations ◽  
Global Analysis ◽  
New Class ◽  
Special Case ◽  
Life Phenomenon

In biology, Difference equations is often used to understand and describe life phenomenon through mathematical models. So, In this work, we study a new class of difference equations by focusing on the periodicity character, stability (local and global) and boundedness of its solutions. Furthermore, this equation involves a May’s Host Parasitoid Model, as a special case.

Group contributions in TU-games: A class of k-lateral Shapley values

2020 ◽  
Vol 286 (2) ◽  
pp. 637-648 ◽  
Author(s):  
Surajit Borkotokey ◽  
Dhrubajit Choudhury ◽  
Loyimee Gogoi ◽  
Rajnish Kumar
Keyword(s):  
Group Contributions ◽  
Tu Games ◽  
Shapley Values

The Need for Permission, the Power to Enforce, and Duality in Cooperative Games with a Hierarchy

2016 ◽  
Vol 18 (04) ◽  
pp. 1650015 ◽  
Author(s):  
Frank Huettner ◽  
Harald Wiese
Keyword(s):  
Cooperative Game ◽  
Cooperative Games ◽  
Transferable Utility ◽  
Tu Game ◽  
Tu Games ◽  
Permission Value

A cooperative game with transferable utility (TU game) captures a situation in which players can achieve certain payoffs by cooperating. We assume that the players are part of a hierarchy. In the literature, this invokes the assumption that subordinates cannot cooperate without the permission of their superiors. Instead, we assume that superiors can force their subordinates to cooperate. We show how both notions correspond to each other by means of dual TU games. This way, we capture the idea that a superiors’ ability to enforce cooperation can be seen as the ability to neutralize her subordinate’s threat to abstain from cooperation. Moreover, we introduce the coercion value for games with a hierarchy and provide characterizations thereof that reveal the similarity to the permission value.

Cooperative Fuzzy Games with Convex Combination Form

2016 ◽  
Vol 33 (01) ◽  
pp. 1650007 ◽  
Author(s):  
Fanyong Meng ◽  
Xiaohong Chen
Keyword(s):  
Convex Combination ◽  
The Other ◽  
New Class ◽  
Shapley Function ◽  
Shapley Values ◽  
Fuzzy Games ◽  
The Difference ◽  
Fuzzy Core ◽  
Cooperative Fuzzy Games ◽  
The Relationship

In this paper, a new class of cooperative fuzzy games named fuzzy games with convex combination form is introduced. This kind of fuzzy games considers two aspects of information. One is the contribution of the players to the associated crisp coalitions; the other is their participation levels. The explicit expression of the Shapley function is given, which is equal to the production of the Shapley function on crisp games and the player participation levels. Meanwhile, the relationship between the fuzzy core and the Shapley function is studied. Surprisingly, the relationship between them does coincide as in crisp case. Furthermore, some desirable properties are researched. Finally, an example is provided to illustrate the difference in fuzzy coalition values and the player Shapley values for four types of fuzzy games.

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