Dividing the Spoils: Incentives for Collective Winning

Abstract

Teams often compete on multiple fronts: parties contest districts for majority control, contractors field specialized units for procurement awards, and squads play match by match for titles. The prize accrues collectively, but incentives depend on its internal division. We study a majoritarian team contest in which two rival managers simultaneously split their team-prize budgets among heterogeneous members, each battle resolved by a homogeneous-of-degree-zero technology. Under a log-odds curvature condition, a unique pure-strategy equilibrium exists: both managers choose identical relative allocations -- whatever the heterogeneity in costs or values -- with each battle's share proportional to its discriminatory power, closeness, and pivotality.