Spectrum of equilibria in Colonel Blotto game

We study Nash equilibria of a symmetric Colonel Blotto game. In this game two players, with N≥1 units of resources each, distribute their resources simultaneously across K≥2 battlefields. We introduce a characteristic of equilibria in this game called spectrum which stands for the fraction of battlefields receiving given numbers of units. We provide complete characterization of spectra of Nash equilibria in Colonel Blotto game when K|N.