They do, often through places like TopCoder, but it's a very expensive way to recruit (not because of prizes but in terms of the amount of employee time taken t

They do, often through places like TopCoder, but it's a very expensive way to recruit (not because of prizes but in terms of the amount of employee time taken to run these things and the risk of it not paying off). The average BigCo already spends in the region of 10-20k per candidate hired, running a graduate recruitment campaigns is an expensive business, so return on investment is an important factor.