Cell polarity refers to the asymmetric distribution of molecular components seen in many cell types. A key regulator of polarity is the Rho GTPase Cdc42. Positive feedback enables concentration of Cdc42 into clusters at the cell cortex, from where they regulate the cytoskeleton. We combine mathematical modeling, including particle-based simulations and reaction-diffusion equations, with experimental investigations to understand the mechanisms that drive polarity establishment in the yeast Saccharomyces cerevisiae. Our investigations reveal conditions for competition between and coexistence of Cdc42 clusters and reveal that the polarity circuit is a bistable system.