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TOPIC:
ON THE OPTIMAL DESIGN OF LOTTERY CONTESTS
ABSTRACT
This paper develops a novel technique that allows us to obtain optimal multiplicative biases for asymmetric Tullock contests - i.e., the weights placed on contestants' effort entries in the contest success function. Generally, Tullock contests with asymmetric valuations have no closed-form solutions when the impact functions are nonlinear. This prevents us from obtaining the optimum by the usual implicit programming approach, which requires an explicit solution to the equilibrium effort profile. We provide an alternative that allows us to circumvent the difficulty without solving for the equilibrium explicitly. Our approach is not limited to total effort maximization, and applies to contest design problems with noncanonical objective functions. Using this approach, we further establish that linear impact functions with zero headstarts are optimal under a broad class of contest objectives when the contest designer is able to choose any form of regular concave impact functions. In another application, we reexamine the classical issue of comparing all-pay auctions and lottery contests under alternative design objectives.