Prize allocation rule ($x_i(b)\ge 0,{\sum }_i{x}_i(b)\le 1$)

A prize allocation rule assigns winning probabilities or divisible prize shares to a profile of efforts. In an all-pay auction, the greatest effort wins; a proportional allocation contest instead assigns shares continuously according to relative effort. The rule is essential data of a contest model.

A winning probability is the probability that a specified participant receives the prize, conditional on the submitted efforts and the allocation rule's randomization.