Working Paper
Group Contests with Endogenous Prize Sharing: Public Goods, Meritocracy, and the Group-Size Paradox with Chen-Yu Pan (2026)
1st round R&R at Social Choice and Welfare
Abstract: This paper examines a group contest model with endogenous prize-sharing rules. Group leaders first determine a prize-sharing rule for their respective groups, specifying both how the prize is allocated between group public goods and private rewards, and how private rewards are distributed—either equally or according to individual contributions. The selected sharing rule is private information and is observed only by members of that group. When leaders aim to maximize their groups? winning probabilities, the optimal sharing rule combines meritocratic rewards with public goods, and the group-size paradox disappears: larger or more cost-efficient teams rely more heavily on a fully meritocratic private component. When leaders maximize group welfare, the equilibrium depends on whether the optimal meritocratic ratio is interior. When the optimum is interior, the public-good share and the meritocratic ratio serve distinct roles: the former determines the value of winning, while the latter implements the desired effort level. The group-size paradox again disappears. If the optimal meritocratic ratio reaches its upper bound, however, the leader must use the private-reward share itself as an incentive instrument. This creates a trade-off between effort incentives and the value of the prize. We derive sufficient conditions under which, for groups at the meritocratic corner, this trade-off causes the group-size paradox to reappear.