| Summary: | I characterize the optimal accuracy level <i>r</i> of an unbiased Tullock contest between two players with heterogeneous prize valuations. The designer maximizes the winning probability of the strong player or the winner’s expected valuation by choosing a contest with an all-pay auction equilibrium (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>r</mi><mo>≥</mo><mn>2</mn></mrow></semantics></math></inline-formula>). By contrast, if she aims at maximizing the expected aggregate effort or the winner’s expected effort, she will choose a contest with a pure-strategy equilibrium, and the optimal accuracy level <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>r</mi><mo><</mo><mn>2</mn></mrow></semantics></math></inline-formula> decreases in the players’ heterogeneity. Finally, a contest designer who faces a tradeoff between selection quality and minimum (maximum) effort will never choose a contest with a semi-mixed equilibrium.
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