# The Power-Dependence Solution to Five Exchange Networks

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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 and divide 24 points, as do nodes and . You can try to equalize dependence within exchanging pairs by controlling the amounts earned by nodes and .

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Contributed by: Phillip Bonacich (March 2011)

Open content licensed under CC BY-NC-SA

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## Details

[1] K. S. Cook and T. Tamagishi, "Power in Exchange Networks: A Power-Dependence Formulation," *Social Networks*, 14(3-4), 1992 pp. 245–265.

[2] R. B. Myerson, *Game Theory: Analysis of Conflict*, Cambridge: Harvard University Press, 1991 p. 454.

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