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Keywords
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Community Structure
Complete Graph
jel code
Myerson Value
Power Measurement
shapley value
Transferable Utility
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Some applications of linear programming methods to the theory of cooperative games
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Harsanyi power solutions for graphrestricted games
Harsanyi power solutions for graphrestricted games,10.1007/s0018200902203,International Journal of Game Theory,René van den Brink,Gerard van der L
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Harsanyi power solutions for graphrestricted games
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Citations: 4
)
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René van den Brink
,
Gerard van der Laan
,
Vitaly Pruzhansky
We consider cooperative
transferable utility
games, or simply TUgames, with limited communication structure in which players can cooperate if and only if they are connected in the communication graph. Solutions for such graph games can be obtained by applying standard solutions to a modified or restricted game that takes account of the cooperation restrictions. We discuss Harsanyi solutions which distribute dividends such that the dividend shares of players in a coalition are based on power measures for nodes in corresponding communication graphs. We provide axiomatic characterizations of the Harsanyi power solutions on the class of cyclefree graph games and on the class of all graph games. Special attention is given to the Harsanyi degree solution which equals the
Shapley value
on the class of
complete graph
games and equals the position value on the class of cyclefree graph games. The
Myerson value
is the Harsanyi power solution that is based on the equal power measure. Finally, various applications are discussed.
Journal:
International Journal of Game Theory  INT J GAME THEORY
, vol. 40, no. 1, pp. 87110, 2011
DOI:
10.1007/s0018200902203
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Citation Context
(2)
...This expression is used to show that the average tree solution with respect to T is a Harsanyi solution (see
van den Brink et al. 2010b
) if and only if T is a subset of the set introduced in Herings et al. (2010)...
...solutions, introduced by Vasil’ev (1982) for TUgames and studied by
van den Brink etal.(2010b)
forcommunicationsituations...
Richard Baron
,
et al.
Average tree solutions and the distribution of Harsanyi dividends
...The graph (N,L) induces 3 trees, one for each of the 3 dierent nodes of N, T(1) = {(1,2),(2,
3
)}, T(2) = {(2,1),(2,3)}, and T(3) = {(3,2),(2,1)}...
...The graph (N,L) induces 3 trees, one for each of the 3 dierent nodes of N, T(1) = {(1,2),(2,3)}, T(2) = {(2,1),(2,
3
)}, and T(3) = {(3,2),(2,1)}...
...The graph (N,L) induces 3 trees, one for each of the 3 dierent nodes of N, T(1) = {(1,2),(2,3)}, T(2) = {(2,1),(2,3)}, and T(3) = {(
3
,2),(2,1)}...
P. Jean Jacques Herings
,
et al.
The average tree solution for cyclefree graph games
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Citations
(4)
Average tree solutions and the distribution of Harsanyi dividends
(
Citations: 1
)
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(
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