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.