Grading on a Curve, and other Effects of Group Size on All-Pay Auctions

We model contests with a fixed proportion of prizes, such as a grading curve, as all-pay auctions where higher effort weakly increases the likelihood of a prize. We find theoretical predictions for the effect of contest size on effort and test our predictions in a laboratory experiment that compares two-bidder auctions with one prize and 20-bidder auctions with ten prizes. Our results demonstrate that larger contests elicit lower effort by low-skilled students, but higher effort by high-skilled. Large contests also generate more accurate rankings of students and more accurate assignment of high grades to the high-skilled.