A compartmentalized bidisperse granular gas clusters competitively [Phys. Rev. Lett. 89, 214301 (2002)]]: By tuning the shaking strength, the clustering can be directed either towards the compartment initially containing mainly small particles or to the compartment containing mainly large particles. Here, the conditions under which this competitive clustering occurs are studied experimentally, numerically (by means of molecular dynamics simulations), and analytically. A minimal model is derived that quantitatively accounts for the observed phenomena.