Apart from the principles and methodologies inherited from Economics and Game Theory, the studies in Algorithmic Mechanism Design typically employ the worst-case analysis and design of approximation schemes of Theoretical Computer Science. For instance, the approximation ratio, which is the canonical measure of evaluating how well an incentive-compatible mechanism approximately optimizes the objective, is defined in the worst-case sense. It compares the performance of the optimal mechanism against the performance of a truthful mechanism, for all possible inputs. In this paper, we take the average-case analysis approach, and tackle one of the primary motivating problems in Algorithmic Mechanism Design—the scheduling problem (Nisan and Ronen, in: Proceedings of the 31st annual ACM symposium on theory of computing (STOC), 1999). One version of this problem, which includes a verification component, is studied by Koutsoupias (Theory Comput Syst 54(3):375–387, 2014). It was shown that the problem has a tight approximation ratio bound of \((n+1)/2\) for the single-task setting, where n is the number of machines. We show, however, when the costs of the machines to executing the task follow any independent and identical distribution, the average-case approximation ratio of the mechanism given by Koutsoupias (Theory Comput Syst 54(3):375–387, 2014) is upper bounded by a constant. This positive result asymptotically separates the average-case ratio from the worst-case ratio. It indicates that the optimal mechanism devised for a worst-case guarantee works well on average.

除了从经济学和博弈论中继承的原理和方法论之外，算法机制设计方面的研究通常采用最坏情况的分析和理论计算机科学的近似方案设计。例如，在最坏的情况下定义了近似比率，该近似比率是评估激励兼容机制近似优化目标的程度的标准度量。对于所有可能的输入，它将最佳机制的性能与真实机制的性能进行比较。在本文中，我们采用平均情况分析，并解决了算法机制设计中的主要动机问题之一—调度问题（Nisan和Ronen，于：第31届ACM计算理论年会论文集（STOC），1999年）。Koutsoupias研究了此问题的一个版本，其中包括验证组件（Theory Comput Syst 54（3）：375–387，2014）。结果表明，对于单任务设置，问题的逼近比为\（（（n + 1）/ 2 \）），其中n是机器数。但是，我们表明，当机器执行任务的成本遵循任何独立且相同的分布时，平均工况近似率Koutsoupias给出的机制（理论计算系统54（3）：375-387，2014年）的上限是一个常数。该肯定结果渐近地将平均情况比率与最坏情况比率分开。这表明为最坏情况的保证而设计的最佳机制平均而言效果很好。