scholarly journals A Necessary and Sufficient Condition for Non-emptiness of the Core of a Non-transferable Utility Game

2002 ◽  
Author(s):  
P. Jean-Jacques Jean-Jacques Herings ◽  
Arkadi Predtetchinski
Keyword(s):  
Sufficient Condition ◽  
Transferable Utility ◽  
Necessary And Sufficient Condition ◽  
The Core ◽  
Transferable Utility Game ◽  
Necessary And Sufficient

scholarly journals Convexity of b-matching Games

2020 ◽  
Author(s):  
Soh Kumabe ◽  
Takanori Maehara
Keyword(s):  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Kidney Exchange ◽  
The Core ◽  
Emptiness Problem ◽  
Matching Games ◽  
Matching Game ◽  
Necessary And Sufficient

The b-matching game is a cooperative game defined on a graph. The game generalizes the matching game to allow each individual to have more than one partner. The game has several applications, such as the roommate assignment, the multi-item version of the seller-buyer assignment, and the international kidney exchange. Compared with the standard matching game, the b-matching game is computationally hard. In particular, the core non-emptiness problem and the core membership problem are co-NP-hard. Therefore, we focus on the convexity of the game, which is a sufficient condition of the core non-emptiness and often more tractable concept than the core non-emptiness. It also has several additional benefits. In this study, we give a necessary and sufficient condition of the convexity of the b-matching game. This condition also gives an O(n log n + m α(n)) time algorithm to determine whether a given game is convex or not, where n and m are the number of vertices and edges of a given graph, respectively, and α(・) is the inverse-Ackermann function. Using our characterization, we also give a polynomial-time algorithm to compute the Shapley value of a convex b-matching game.

THE EGALITARIAN NON-k-AVERAGED CONTRIBUTION (ENkAC-) VALUE FOR TU-GAMES

1999 ◽  
Vol 01 (01) ◽  
pp. 45-61 ◽  
Author(s):  
TSUNEYUKI NAMEKATA ◽  
THEO S. H. DRIESSEN
Keyword(s):  
Solution Concept ◽  
Sufficient Condition ◽  
Individual Contribution ◽  
Transferable Utility ◽  
Tu Games ◽  
The Core ◽  
Centre Of Gravity ◽  
Transferable Utility Game ◽  
Individual Contributions ◽  
Transferable Utility Games

This paper deals in a unified way with the solution concepts for transferable utility games known as the Centre of the Imputation Set value (CIS-value), the Egalitarian Non-Pairwise-Averaged Contribution value (ENPAC-value) and the Egalitarian Non-Separable Contribution value (ENSC-value). These solutions are regarded as the egalitarian division of the surplus of the overall profits after each participant is conceded to get his individual contribution specified in a respective manner. We offer two interesting individual contributions (lower- and upper-k-averaged contribution) based on coalitions of size k(k ∈ {1,…,n-1}) and introduce a new solution concept called the Egalitarian Non-k-Averaged Contribution value ( EN k AC -value). CIS-, ENPAC- and ENSC-value are the same as EN 1 AC -, EN n-2 AC - and EN n-1 AC -value respectively. It turns out that the lower- and the upper-k-averaged contribution form a lower- and an upper-bound of the Core respectively. The Shapley value is the centre of gravity of n-1 points; EN 1 AC -,…, EN n-1 AC -value. EN k AC -value of the dual game is equal to EN n-k AC -value of the original game. We provide a sufficient condition on the transferable utility game to guarantee that the EN k AC -value coincides with the well-known solution called prenucleolus. The condition requires that the largest excesses at the EN k AC -value are attained at the k-person coalitions, whereas the excesses of k-person coalitions at the EN k AC -value do not differ.

A NECESSARY AND SUFFICIENT CONDITION FOR THE NON-EMPTINESS OF THE SOCIALLY STABLE CORE IN STRUCTURED TU-GAMES

2009 ◽  
Vol 11 (03) ◽  
pp. 383-389
Author(s):  
JUAN CARLOS CESCO
Keyword(s):  
Sufficient Condition ◽  
Transferable Utility ◽  
Tu Game ◽  
Necessary And Sufficient Condition ◽  
Tu Games ◽  
Classical Condition ◽  
Stable Core ◽  
Necessary And Sufficient

In this note we provide a neccesary and sufficient condition for the non-emptiness of the socially stable core of a general structured TU-game which resembles closely the classical condition of balancedness given by Bondareva (1963) and Shapley (1967) to guarantee the non-emptiness of the classical core. Structured games have been introduced in Herings et al. (2007a) and more recently, in Herings et al. (2007b), studied in the framework of games with transferable utility. In the latter paper, the authors provide suffcient conditions for the non-emptiness of the socially stable core, but up to now, no necessary and sufficient condition is known.

A Proposed Framework Emphasizing Auditor Reliability over Auditor Independence

2003 ◽  
Vol 17 (3) ◽  
pp. 257-266 ◽  
Author(s):  
Mark H. Taylor ◽  
F. Todd DeZoort ◽  
Edward Munn ◽  
Martha Wetterhall Thomas
Keyword(s):  
Public Interest ◽  
Auditor Independence ◽  
Public Confidence ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Accounting Profession ◽  
The Public ◽  
Necessary And Sufficient

This paper introduces an auditor reliability framework that repositions the role of auditor independence in the accounting profession. The framework is motivated in part by widespread confusion about independence and the auditing profession's continuing problems with managing independence and inspiring public confidence. We use philosophical, theoretical, and professional arguments to argue that the public interest will be best served by reprioritizing professional and ethical objectives to establish reliability in fact and appearance as the cornerstone of the profession, rather than relationship-based independence in fact and appearance. This revised framework requires three foundation elements to control subjectivity in auditors' judgments and decisions: independence, integrity, and expertise. Each element is a necessary but not sufficient condition for maximizing objectivity. Objectivity, in turn, is a necessary and sufficient condition for achieving and maintaining reliability in fact and appearance.

The Power of Public Positions

2018 ◽  
Author(s):  
Thomas Sinclair
Keyword(s):  
Detailed Analysis ◽  
Political Authority ◽  
The State ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
State Institutions ◽  
State Of Nature ◽  
Necessary And Sufficient

The Kantian account of political authority holds that the state is a necessary and sufficient condition of our freedom. We cannot be free outside the state, Kantians argue, because any attempt to have the “acquired rights” necessary for our freedom implicates us in objectionable relations of dependence on private judgment. Only in the state can this problem be overcome. But it is not clear how mere institutions could make the necessary difference, and contemporary Kantians have not offered compelling explanations. A detailed analysis is presented of the problems Kantians identify with the state of nature and the objections they face in claiming that the state overcomes them. A response is sketched on behalf of Kantians. The key idea is that under state institutions, a person can make claims of acquired right without presupposing that she is by nature exceptional in her capacity to bind others.

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