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

Abstract

This study examines the mechanism design problem for public goods in a model with independent private values. We propose a class of informationally robust, dominant-strategy incentive compatible (DSIC), and ex post individual rational (EPIR) mechanisms that are asymptotically ex ante budget balanced (AEABB) and asymptotically efficient (AE) as the population grows. The decision rule is constructed in two steps: First, each valuation is transformed with an increasing function and centered to be mean zero. Then the public good is allocated if the sum of transformed valuations exceeds a threshold that only depends on the population size n. The increasing function can be chosen arbitrarily. For example, it can simply be the identity function.Our results show that the rate of change of the threshold is the key to characterizing the tradeoff between budget balance and efficiency. In particular, using the multivariate Berry-Esseen theorem, our results demonstrate that when this rate is controlled within the range of √ n to √ n log n, the mechanism can be AEABB and AE at the same time as long as the cost does not grow too rapidly. One advantage of the proposed mechanisms is their informational robustness as they depend only on certain moments of the valuation distributions. In contrast, previous mechanisms proposed to solve this question, such as the second-best mechanism, typically require the knowledge of the entire valuation distribution. Also, our study extends the results to non-binary decision environments with general utility functions. Lastly, we show that if the threshold is instead set equal to the cost, the proposed mechanism can achieve a non-negligible fraction of the optimal profit in the limit, where the fraction is the correlation between the virtual value and the aforementioned transformed value.