The multiexciton density matrix theory is utilized to achieve a microscopic description of exciton-exciton annihilation (EEA). We apply the theory to the 18 bacteriochlorophyll (BChl) molecules of the B850 ring of the light-harvesting complex LH2 of Rhodobacter sphaeroides. The simulation of the EEA process reproduces the intensity-dependent transient absorption kinetic experiments very well, and insight is obtained on microscopic parameters such as the internal conversion rate of BChl in LH2. The exciton dynamics and the different relaxation processes are visualized by constructing a multiexciton spectrogram.