When is a contest "additive"? A characterization of strategic equivalence

We characterize the production technologies that generate contests strategically equivalent to the standard additive Lazear-Rosen tournament. A contest with a general production function is strategically equivalent to the additive benchmark if and only if the marginal rate of technical substitution (MRTS) between effort and skill is multiplicatively separable, a characterization that links strategically equivalent contests to the classical theory of additive utility representations. The equivalence class is large: it contains the multiplicative, Cobb-Douglas, CES, and quasilinear technologies, so that, within the class, additivity is a normalization rather than an economic assumption, and existing results for additive contests, e.g., on optimal prize structures and on the effects of noise on effort, extend to the entire class. Strategic equivalence does not, however, make the technology irrelevant for contest design: the equivalence preserves only ordinal information, whereas optimal prize structures depend on cardinal features of the environment. Strategically equivalent technologies can therefore call for opposite prize structures under the same skill distribution. In particular, when skills are exponentially distributed, the case in which all prize structures perform equally well in the additive model, the monotonicity of the MRTS in skill alone determines whether the winner-takes-all or the loser-gets-nothing contest is optimal.