Competition between groups often involves prizes that have both a public and a private component. The exact nature of the prize not only affects the strategic choice of the sharing rules determining its allocation but also gives rise to an interesting phenomenon not observed when the prize is either purely public or purely private. Indeed, we show that in the two-groups contest, for most degrees of privateness of the prize, the large group uses its sharing rule as a mean to exclude the small group from the competition, a situation called monopolization. Conversely, there is a degree of relative privateness above which the small group, besides being active, even outperforms the large group in terms of winning probabilities, giving rise to the celebrated group size paradox.

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We study the decentralization of redistributive taxation in a political economy model assuming regional heterogeneity regarding both group identity and average income. If a centralized system permits a beneficial pooling of national resources, it might also decrease the degree of solidarity in the society. With no group loyalty, centralization Pareto-dominates decentralization even when regions are not identical. Furthermore, increased heterogeneity need not increase the relative efficiency of decentralization. If regions are equally rich, centralization Pareto-dominates decentralization whenever group loyalty is not perfect. Finally, centralization is always more efficient than decentralization even when allowing for interregional transfers.JEL Codes: H77, D64, H23