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We study a two-stage Tullock contest with asymmetric players where a designer allocates a productivity-enhancing advantage based on past performance. The advantage’s magnitude is exogenously fixed, so the designer’s choice is purely allocative: who receives it. We characterize the optimal rule and show a sharp threshold in asymmetry. With moderate heterogeneity, favouring the stage-1 winner strengthens incentives and maximises total effort. With sufficiently large heterogeneity, favouring the stage-1 loser restores competitiveness in stage 2 and raises aggregate effort. The results clarify optimal contest design under limited favouritism instruments.
Ngoc Anh Pham (Wed,) studied this question.