An algebraic theory of strong power in negatively connected exchange networks

Phillip Bonacich, Motoki Watabe

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A structural and algebraic theory of power in negatively connected exchange networks can be deduced from a few simple and plausible assumptions about how individuals make decisions. The model generates a set of equations. A typology of exchange networks follows from characteristics of the solution to these equations. There are four possibilities: the equations have a unique solution in which some positions have all the power; the equations have a unique solution in which all positions have equal power; the equations have an infinity of solutions, in which case power is undetermined by structural considerations; the equations have no solution, in which case power should be unstable. Various extensions of the model are proposed to deal with a wider variety of conditions than a normally examined in experiments on exchange networks. With little or no modification, the model can predict power when exchange relations are unequal in value, when positions vary in the number of exchanges in which they can participate, and when three or more participants are required for a transaction to occur.

Original languageEnglish
Pages (from-to)33-52
Number of pages20
JournalSociological Theory and Methods
Issue number1
Publication statusPublished - Mar 2003
Externally publishedYes


  • Exchange
  • Networks
  • Power

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