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===Additive Noise===
Consider a problem with two risk neutral contestants where the observation of effort is based on the actual effort plus some idiosyncratic noise, that is <math>x_i + \epsilon_i \forall i \,</math> is observed. Letting <math>\epsilon = \epsilon_2 - \epsilon_1 \,</math> we can write the contest success function as:
<math>
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