On optimal mechanism design for a sequencing problem

Abstract

We study mechanism design for a single-server setting where jobs require compensation for waiting, while waiting cost is private information to the jobs. With given priors on the private information of jobs, we aim to find a Bayes-Nash incentive compatible mechanism that minimizes the total expected payments to the jobs. Following earlier work in the auction literature, we show that this problem is solved, in polynomial time, by a version of Smith's rule. When both waiting cost and processing times are private, we show that optimal mechanisms generally do not satisfy an independence condition known as IIA, and conclude that a closed form for optimal mechanisms is generally not conceivable.

Mechanisms for scheduling games with selfish players

“…Then the start times, S j (t i j , t −j ), need to be monotonically increasing in the reported weight, w i j , for all t −j ∈ T −j . This is a standard result in single-dimensional mechanism design, see for instance the introductory text by Nisan [53], but it is also true for the two-dimensional problem considered here [33,19].…”

“…For the single-dimensional mechanism design problem, where only weights w j are private information and processing times p j are known, the optimal mechanism has a simple structure: It is Smith's rule, but with respect to virtual instead of original weights w j ; see Heydenreich et al [33] and Duives et al [19] for details. In this case the optimal Bayes-Nash incentive compatible mechanism can be computed and implemented in polynomial time, and it can even be implemented with the same expected cost in dominant strategies [19].…”

“…In this case the optimal Bayes-Nash incentive compatible mechanism can be computed and implemented in polynomial time, and it can even be implemented with the same expected cost in dominant strategies [19].…”

“…The problem to find and analyze an optimal mechanism for the two-dimensional optimal mechanism design problem was left open by Heydenreich et al [33] and Duives et al [19].…”

“…Our computations, based on randomly generated instances, show that optimal mechanisms in the two-dimensional setting do not share several of the nice properties of the solutions to the single-dimensional problem: The scheduling rules of optimal Bayes-Nash incentive compatible mechanisms are not necessarily IIA (a desirable property to be defined later), and neither do optimal Bayes-Nash mechanisms allow an implementation in dominant strategies. This in contrast to the single-dimensional problem which does have these properties [33,19].…”