scholarly journals The average covering tree value for directed graph games

2019 ◽  
Vol 39 (2) ◽  
pp. 315-333 ◽  
Author(s):  
Anna Khmelnitskaya ◽  
Özer Selçuk ◽  
Dolf Talman
Keyword(s):  
Directed Graph ◽  
Undirected Graph ◽  
Solution Concept ◽  
Transferable Utility ◽  
Communication Structure ◽  
Gravity Center ◽  
Dominance Relations ◽  
Graph Games ◽  
Covering Tree ◽  
Transferable Utility Games

Abstract We introduce a single-valued solution concept, the so-called average covering tree value, for the class of transferable utility games with limited communication structure represented by a directed graph. The solution is the average of the marginal contribution vectors corresponding to all covering trees of the directed graph. The covering trees of a directed graph are those (rooted) trees on the set of players that preserve the dominance relations between the players prescribed by the directed graph. The average covering tree value is component efficient, and under a particular convexity-type condition it is stable. For transferable utility games with complete communication structure the average covering tree value equals to the Shapley value of the game. If the graph is the directed analog of an undirected graph the average covering tree value coincides with the gravity center solution.

scholarly journals The Average Covering Tree Value for Directed Graph Games

2012 ◽  
Author(s):  
Anna Khmelnitskaya ◽  
Özer Selcuk ◽  
Dolf J. J. Talman
Keyword(s):  
Directed Graph ◽  
Graph Games ◽  
Covering Tree

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.

Two Streamlined Depth-First Search Algorithms

1986 ◽  
Vol 9 (1) ◽  
pp. 85-94
Author(s):  
Robert Endre Tarjan
Keyword(s):  
Directed Graph ◽  
Graph Algorithms ◽  
Undirected Graph ◽  
Linear Time ◽  
Search Algorithms ◽  
Depth First Search ◽  
Time Graph

Many linear-time graph algorithms using depth-first search have been invented. We propose simplified versions of two such algorithms, for computing a bipolar orientation or st-numbering of an undirected graph and for finding all feedback vertices of a directed graph.

scholarly journals THE POSITIVE PREKERNEL OF A COOPERATIVE GAME

2000 ◽  
Vol 02 (04) ◽  
pp. 287-305 ◽  
Author(s):  
PETER SUDHÖLTER ◽  
BEZALEL PELEG
Keyword(s):  
Cooperative Game ◽  
Weak Version ◽  
Transferable Utility ◽  
Bargaining Set ◽  
The Core ◽  
Reduced Game ◽  
Positive Kernel ◽  
Game Property ◽  
Transferable Utility Games

The positive prekernel, a solution of cooperative transferable utility games, is introduced. We show that this solution inherits many properties of the prekernel and of the core, which are both sub-solutions. It coincides with its individually rational variant, the positive kernel, when applied to any zero-monotonic game. The positive (pre)kernel is a sub-solution of the reactive (pre)bargaining set. We prove that the positive prekernel on the set of games with players belonging to a universe of at least three possible members can be axiomatized by non-emptiness, anonymity, reasonableness, the weak reduced game property, the converse reduced game property, and a weak version of unanimity for two-person games.

scholarly journals Tree-Type Values for Cycle-Free Directed Graph Games

2010 ◽  
Author(s):  
Dolf J. J. Talman ◽  
Anna B. Khmelnitskaya
Keyword(s):  
Directed Graph ◽  
Graph Games ◽  
Tree Type

scholarly journals Axiomatic results and dynamic processes for two weighted indexes under fuzzy transferable-utility behavior

2022 ◽  
Vol 12 (1) ◽  
pp. 1
Author(s):  
Yu-Hsien Liao
Keyword(s):  
Dynamic Processes ◽  
Excess Functions ◽  
Transferable Utility ◽  
Transferable Utility Games

<p style='text-indent:20px;'>By considering the supreme-utilities and the weights simultaneously under fuzzy behavior, we propose two indexes on fuzzy transferable-utility games. In order to present the rationality for these two indexes, we define extended reductions to offer several axiomatic results and dynamics processes. Based on different consideration, we also adopt excess functions to propose alternative formulations and related dynamic processes for these two indexes respectively.</p>

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