A contest success function with a rent-dependent dissipation rate

In this note a new contest success function is derived that results in investments in equilibrium that are proportional to the square of the rent, which implies a dissipation rate that is not independent of, but increasing in the rent. Only for a contest success function with this property can it be optimal to use least squares regression models to determine transfers for a risk adjustment scheme (a regulatory means to reduce risk selection in health insurance markets). A second property of this new contest success function is that winning probabilities do not depend only on the ratio or only on the difference of investments, but on both the ratio and the difference; this may make it more suitable than common contest success functions for some situations like corruption or getting tenure at a university.