Selective Incentives and Intra-Group Heterogeneity in Collective Contents

A group taking part in a contest has to confront the collective-action problem among its members and devices of selective incentives are possible means of resolution. We argue that heterogeneous prize-valuations in a competing group normally prevent effective use of such selective incentives. To substantiate this claim, we adopt cost sharing as a means of incentivizing the individual group members. We confirm that homogeneous prize valuations within a group result in a cost-sharing rule inducing the first-best individual contributions. As long as the cost-sharing rule is dependent only on the members' contributions, however, such a first-best rule does not exist for a group with intra-group heterogeneity. Our main result clarifies how unequal prize valuations affect the cost-sharing rule and, in particular, the degree of cost sharing. The results are related to the fact that heterogeneous valuations of the prize in a group cause inappropriate realization of voluntary contributions, a situation known as the "exploitation of the great by the small."