In this paper I propose structural criteria for power based only on si
mple and valid assumptions about how individuals in exchange networks
make decisions. The implication of the model is that exchange networks
contain four types of components, identified by the solution to a set
of equations. In coreless components, the equations are inconsistent
and trading behavior is unstable In strong power components, the equat
ions have a unique solution and some positions have complete power. In
equal power components, the equations have a unique solution, and all
positions are equal in power: In indeterminate components, the equati
ons have an infinity of solutions and power is not determined strongly
by structure. Formal criteria are developed for these four types of c
omponents.