We extend network exchange theory (Markovsky, Willer, and Patton 1988)
to accommodate a new class of power phenomena. Previous theory and re
search have shown that structural configurations in some networks prom
ote or inhibit exchange opportunities, leading to robust power and res
ource differentials. The extension identifies a structural basis for s
ubtler forms of differentiation. Using computer simulations and labora
tory experiments, we show that the degree to which this ''weak power''
is manifested in resource accumulations is conditioned by local and g
lobal network patterns, and by the experience and strategies of actors
in the network. Experimental tests corroborate the predicted weak pow
er effects and the consequences of variations in actors' negotiating e
xperiences.