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The Power-Dependence Solution to Five Exchange Networks

C's share
12
B's share
12
4-line network
kite network
5-line network
tee network
hourglass network
The power-dependence solution to exchange networks assumes that both members of every exchange have equally good alternatives outside the exchange; this solution is an application of the game-theoretic concept of the kernel [2] to exchange networks. All the illustrated networks have four or five nodes and all exchanges are worth 24 points. In every network, nodes
A
and
B
divide 24 points, as do nodes
C
and
D
. You can try to equalize dependence within exchanging pairs by controlling the amounts earned by nodes
B
and
C
.
For example, in the 4-line network let
B
earn 16 in a trade with
A
, who earns 8, and let
C
earn 16 in a trade with
D
, who earns 8. If
B
leaves
A
for
C
, his only alternative partner, he will have to offer
C
at least 16 points and
B
will earn the remaining 8, 8 less than he was earning.
A
, who has no alternative partner, will receive nothing, 8 less than what he was earning.
A
and
B
, then, are equally harmed by a change, as are
C
and
D
. This is the power-dependence solution.
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