We study the classic public project problem, where the agents decide whether or not to build a non-excludable public project. We focus on efficient, strategy-proof, and weakly budget-balanced mechanisms (VCG redistribution mechanisms). Our aim is to maximize the worst-case efficiency ratio—the worst-case ratio between the achieved total utility and the first-best maximum total utility. Previous studies have identified an optimal mechanism for 3 agents. Unfortunately, no optimal mechanisms have been identified for more than 3 agents. We propose an automated mechanism design approach that is capable of handling worst-case objectives. With its help, we identify a different optimal mechanism for 3 agents. For more agents, we identify mechanisms with better worst-case efficiency ratios than previous results. Using a dimension reduction technique, we extend the newly identified optimal mechanism for 3 agents to n agents. The resulting mechanism’s worst-case efficiency ratio equals \(\frac{n+1}{2n}\). In comparison, the best previously known worst-case efficiency ratio equals 0.102 asymptotically. We then derive an asymptotically optimal mechanism under a minor technical assumption: we assume the agents’ valuations are rational numbers with bounded denominators. Previous studies conjectured that the optimal asymptotic worst-case efficiency ratio equals 1. We confirm this conjecture.

我们研究了经典的公共项目问题，其中代理决定是否构建非排他性公共项目。我们专注于有效的、战略性的和弱预算平衡机制（VCG 再分配机制）。我们的目标是最大化最坏情况下的效率比——达到的总效用与第一个最佳的最大总效用之间的最坏情况比率。以前的研究已经确定了 3 种药物的最佳机制。不幸的是，没有为超过 3 个代理确定最佳机制。我们提出了一种能够处理最坏情况的自动化机制设计方法目标。在它的帮助下，我们为 3 个代理确定了不同的最佳机制。对于更多的代理，我们确定了比以前的结果具有更好的最坏情况效率比的机制。使用降维技术，我们将新确定的 3 个代理的最佳机制扩展到n 个代理。由此产生的机制的最坏情况效率比等于\(\frac{n+1}{2n}\)。相比之下，先前已知的最坏情况下的最佳效率比渐近地等于 0.102。然后，我们在一个次要的技术假设下推导出渐近最优机制：我们假设代理的估值是具有有界分母的有理数。先前的研究推测，最佳渐近最坏情况效率比等于 1。我们证实了这一猜想。