A technique is described for assigning a location-finder role to a mobile computing device (a “location-finder device”) within a spatially-clustered group of mobile computing devices. The location-finder device determines its location based on signals received from one or more external sources (such as a GPS system), to provide location data. The location-finder device then transmits a signal to other members of the group of mobile computing devices using a local communication channel (such as a BLUETOOTH communication channel). That signal conveys the location data. Each of the other members of the group uses the location data to define its position, in lieu of independently determining its own location from the external source(s). By virtue of this behavior, the other members can reduce their consumption of power.