Returns to effort in rent-seeking games

In the traditional formulation of rent-seeking games, increasing returns to effort are characterized by an exponent r > 1. However, when the value of the rent is normalized to 1, the players' effort levels A and B will typically be less than 1. Thus, when A < 1 and r > 1, the value of Ar decreases as r increases, contradicting the interpretation of r > 1 as representing increasing returns to effort. This apparent defect in the mathematization of the problem seems to suggest that a different interpretation of r is required whenever A < 1, upsetting the uniformity and elegance of the model. In this short note, we demonstrate that the perceived problem is illusory, and that the usual interpretation of r is satisfactory for all values of A.