Average-case Approximation Ratio of Scheduling without Payments

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 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 1999]. One version of this problem which includes a verification component is studied by [Koutsoupias 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 in [Koutsoupias 2014] is upper bounded by a constant. This positive result asymptotically separates the average-case ratio from the worst-case ratio, and indicates that the optimal mechanism for the problem actually works well on average, although in the worst-case the expected cost of the mechanism is Theta(n) times that of the optimal cost

Optimal and Efficient Auctions for the Gradual Procurement of Strategic Service Provider Agents

We consider an outsourcing problem where a software agent procures multiple services from providers with uncertain reliabilities to complete a computational task before a strict deadline. The service consumer’s goal is to design an outsourcing strategy (defining which services to procure and when) so as to maximize a specific objective function. This objective function can be different based on the consumer’s nature; a socially-focused consumer often aims to maximize social welfare, while a self-interested consumer often aims to maximize its own utility. However, in both cases, the objective function depends on the providers’ execution costs, which are privately held by the self-interested providers and hence may be misreported to influence the consumer’s decisions. For such settings, we develop a unified approach to design truthful procurement auctions that can be used by both socially-focused and, separately, self-interested consumers. This approach benefits from our proposed weighted threshold payment scheme which pays the provably minimum amount to make an auction with a monotone outsourcing strategy incentive compatible. This payment scheme can handle contingent outsourcing plans, where additional procurement happens gradually over time and only if the success probability of the already hired providers drops below a time-dependent threshold. Using a weighted threshold payment scheme, we design two procurement auctions that maximize, as well as two low-complexity heuristic-based auctions that approximately maximize, the consumer’s expected utility and expected social welfare, respectively. We demonstrate the effectiveness and strength of our proposed auctions through both game-theoretical and empirical analysis

Average-case approximation ratio of scheduling without payments

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.</p