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

TL;DR

This paper introduces the adjusted mean-thresholding (AMT) mechanisms for public goods provision in large economies, demonstrating their efficiency and robustness under certain growth conditions of provision costs.

Contribution

The paper proposes a new class of incentive-compatible mechanisms that are simple, robust, and effective for large economies, extending the mechanism design theory for public goods.

Findings

AMT mechanisms are ex-ante budget balanced and asymptotically efficient when costs grow slower than √n.

When costs grow faster than √n, no mechanism can be asymptotically efficient, and provision probability tends to zero.

AMT mechanisms depend only on the first moment of valuation distribution, enhancing informational robustness.

Abstract

This study examines the mechanism design problem for public goods provision in a large economy with $n$ independent agents. We propose a class of dominant-strategy incentive compatible and ex-post individually rational 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 eventually ex-ante budget balanced and asymptotically efficient. When the cost grows faster than the $\sqrt{n}$-rate, in contrast, we show that any incentive compatible, individually rational, and eventually ex-ante budget balanced mechanism must have provision probability converging to zero and hence cannot be asymptotically efficient. The AMT mechanisms have a simple form and are more informationally robust when compared to, for example, the second-best mechanism. This is because the construction of an AMT mechanism depends only on the first moment of the valuation distribution.