Strength in Numbers: Robust Mechanisms for Public Goods with Many Agents

This study examines the mechanism design problem for public-good provision in a large economy with $n$ independent agents. We propose a class of dominant-strategy incentive compatible (DSIC) and ex post individual rational (EPIR) mechanisms which we call the adjusted mean-thresholding (AMT) mechanisms. We show that when the cost of provision grows slower than the $sqrt{n}$ rate, the AMT mechanisms are both asymptotically ex ante budget balanced (AEABB) and asymptotically efficient (AE). When the cost grows faster than the $sqrt{n}$ rate, in contrast, we show that any DSIC, EPIR, and AEABB mechanism must have provision probability converging to zero and hence cannot be AE. Lastly, the AMT mechanisms are more informationally robust when compared to, for example, the second-best mechanism. This is because the construction of AMT mechanisms depends only on the first moments of the valuation distributions.