Competitive accretion occurs when stars in a cluster accrete from a shared reservoir of gas .
The competition arises due to the relative attraction of stars as a function of their mass and location in the cluster .
The low relative motions of the stars and gas in young , gas dominated clusters results in a tidal limit to the accretion whereas in the stellar dominated cluster cores , the high relative velocities results in Bondi-Hoyle accretion .
The combination of these two accretion processes produces a two power-law IMF with \gamma \approx - 1.5 , for low-mass stars which accrue their mass in the gas dominated regime , and a steeper , \gamma \approx - 2.5 , IMF for higher-mass stars that form in the core of a cluster .
Simulations of the fragmentation and formation of a stellar cluster show that the final stellar masses , and IMF , are due to competitive accretion .
Competitive accretion also naturally results in a mass segregated cluster and in a direct correlation between the richness of a cluster and the mass of the most massive star therein .
The knee where the IMF slope changes occurs near the Jeans mass of the system .