New contest success functions

Skaperdas (1996) characterized the contest success function (CSF), which stipulates the winning probabilities of the contestants, using respectively the scale invariance and translation invariance axioms. This paper first characterizes the entire family of CSFs that fulfils a convex mixture of the two axioms. This family contains the Skaperdas CSFs as special cases. Next, we consider two ordinal axioms, scale consistency and translation consistency, and characterize the respective classes of CSFs. While the former consists of the Skaperdas scale invariant and translational invariant CSFs and some new functional forms, the latter contains the Skaperdas translation invariant CSF and some additional CSFs that were not considered in the literature earlier.