We analyze the magnetic behavior of well-characterized, precipitate-free Ga1-xMnxN thin films containing Mn at higher levels than previously attained; up to x=0.36. This level is above the percolation threshold x(c) for nearest-neighbor cations, such that exchange between nearest neighbors will dominate the magnetic response. The susceptibility decreases as the Mn content increases up to and beyond xc, as an increasing fraction of the Mn experiences antiferromagnetic exchange. The dominance of antiferromagnetic behavior at higher Mn concentrations and the total lack of evidence for ferromagnetic ordering even above xc demonstrates that the nature of the exchange between Mn2+ ions in GaN is antiferromagnetic.