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This article proposes a stochastic foundation for the contest success function (CSF for short) with a richer structure on the set of possible outcomes of the contest. Specifically, the analysis allows for the possibility of a draw, so that no contestant can claim a victory over all other players. Under plausible conditions, this article not only discovers new functional forms of CSFs, but also shows the newly derived CSFs have very different properties in equilibrium to those of conventional CSFs. For example, in contrast to the CSFs discussed in the contest literature, which always generate a unique pure strategy Nash equilibrium, the newly discovered CSFs admit the possibility of multiple equilibria.
