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

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 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

The Myerson value for directed graph games

2020 ◽  
Vol 48 (2) ◽  
pp. 142-146
Author(s):  
Daniel Li Li ◽  
Erfang Shan
Keyword(s):  
Directed Graph ◽  
Myerson Value ◽  
Graph Games

Tree, web and average web values for cycle-free directed graph games

2014 ◽  
Vol 235 (1) ◽  
pp. 233-246 ◽  
Author(s):  
Anna Khmelnitskaya ◽  
Dolf Talman
Keyword(s):  
Directed Graph ◽  
Graph Games

scholarly journals The Shapley Value for Directed Graph Games

2014 ◽  
Author(s):  
Anna Khmelnitskaya ◽  
zer Selcuk ◽  
Dolf Talman
Keyword(s):  
Directed Graph ◽  
Shapley Value ◽  
Graph Games ◽  
The Shapley Value

scholarly journals The Shapley value for directed graph games

2016 ◽  
Vol 44 (1) ◽  
pp. 143-147 ◽  
Author(s):  
Anna Khmelnitskaya ◽  
Özer Selçuk ◽  
Dolf Talman
Keyword(s):  
Directed Graph ◽  
Shapley Value ◽  
Graph Games ◽  
The Shapley Value
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