A stochastic derivation of the ratio form of contest success functions

This note provides a distribution-based justification for the ratio form of contest success functions (CSFs), in which a player’s success depends positively on her effort relative to that of her opponents. I show that the inverse exponential distribution of the random shocks yields the ratio form. Extending this approach to asymmetric contests, I also derive an asymmetric ratio form of CSFs. <br />