Rebate Rules in Large Group Threshold Public Goods Experiments: The Role of Uncertainty and Beliefs

This paper explores multi-round threshold public goods provision in large groups. We elicit subjects' beliefs regarding others' contributions and the project's cost; and we vary the amount of information between Round-0 and subsequent rounds to examine how the demand revelation changes with information, repetition, and cost. Our Round-0 decision-task replicates the large-group one-shot game of Rondeau et al. (1999) and Spencer et al. (2009), in which the project cost and group members' value distribution are unknown to subjects. In addition to the proportional rebate and three winner-take-all policies (Spencer et al., 2009), we introduce and compare two novel rebate rules: the uniform price cap (UPC) and the uniform price auction (UPA) mechanisms. Our Round-0 result shows that, in the one-shot unknown-cost setup, all rebate policies induce group contributions higher than the actual cost. Nonetheless, only UPC and UPA achieve almost 100\% demand revelation, while the demand revelation under all other rebate policies is significantly below 100\%. This result is different from Rondeau et al. (1999) and Spencer et al. (2009), which suggest 100\% or more demand revelation for most rebate policies under the one-shot large-group design. Interestingly, subjects' perceived cost is not significantly different from their induced values for all mechanisms but two winter-take-all policies. Subjects contribute significantly less than their perceived cost except for UPC and UPA treatments. Furthermore, in the subsequent rounds when the cost information is revealed and decisions are repeated, full demand revelation disappears. Group contributions increase with cost; yet the rates for successful provision decrease.