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Mathematical Programming Approach to Multidimensional Mechanism Design for Single Machine Scheduling

By Jelle Duives and Marc Uetz


We consider the following optimal mechanism design problem in single machine scheduling. Given are n jobs which we regard as selfish agents. Jobs need to be processed non-preemptively on a single machine. Each job j has processing time pj and a disutility wj for waiting one unit of time. This defines the 2-dimensional type tj = (wj, pj) of a job j. The allocation rule f is a mapping of type profiles t = (tj)j=1,...,n to the set of all n! sched-ules. If in a given schedule σ, Sj(σ) denotes the starting time of job j, the jobs valuation for that schedule is −wjSj(σ). We assume that the mechanism designer needs to compensate jobs for waiting in the form of a payment pij, such that pij−wjSj ≥ 0. We consider this problem in a Bayes-Nash setting, that is, given are publicly known, discrete probability distributions describ-ing the jobs ’ possible types. Our goal is to find a (Bayes-Nash) incentive compatible mechanism that is optimal, which is a mechanism that minimizes the total expected payment j Epij. This Problem has been considered earlier in a paper by Heydenreich et al. [3], where mainly the special case of 1-dimensional type spaces has been analyzed (that is, public processing times pj and private wj). Also in that paper, an example has been proposed to show tha

Year: 2016
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