Birgit Heydenreich

Characterization of Revenue Equivalence

A saw blade guard for a sawing power tool, particularly a mitre saw, comprises a protective element having two side walls each formed as a part of a circle, and a peripheral wall connecting the side walls with one another, the side walls having a center and an edge spaced from the center, the protective element being formed as an integral element and provided with a member in the region of the edge for turning the protective element as a whole.

On optimal mechanism design for a sequencing problem

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.

Mechanism Design for Decentralized Online Machine Scheduling

Traditional optimization models assume a central decision maker who optimizes a global system performance measure. However, problem data is often distributed among several agents, and agents make autonomous decisions. This gives incentives for strategic behavior of agents, possibly leading to suboptimal system performance. Furthermore, in dynamic environments, machines are locally dispersed and administratively independent. Examples are found both in business and engineering applications. We investigate such issues for a parallel machine scheduling model where jobs arrive online over time. Instead of centrally assigning jobs to machines, each machine implements a local sequencing rule and jobs decide for machines themselves. In this context, we introduce the concept of a myopic best-response equilibrium, a concept weaker than the classical dominant strategy equilibrium, but appropriate for online problems. Our main result is a polynomial time, online mechanism that---assuming rational behavior of jobs---results in an equilibrium schedule that is 3.281-competitive with respect to the maximal social welfare. This is only slightly worse than state-of-the-art algorithms with central coordination.