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Maximizing the Minimum Load for Selfisch Agents Epstein, Leah van Stee, Rob Scheduling algorithmic mechanism design maximizing minimum load We consider the problem of maximizing the minimum load for machines that are controlled by selfish agents, who are only interested in maximizing their own profit. Unlike the classical load balancing problem, this problem has not been considered for selfish agents until now. For a constant number of machines, $m$, we show a monotone polynomial time approximation scheme (PTAS) with running time that is linear in the number of jobs. It uses a new technique for reducing the number of jobs while remaining close to the optimal solution. We also present an FPTAS for the classical machine covering problem, i.e., where no selfish agents are involved (the previous best result for this case was a PTAS) and use this to give a monotone FPTAS. Additionally, we give a monotone approximation algorithm with approximation ratio $min(m,(2+eps)s_1/s_m)$ where $eps>0$ can be chosen arbitrarily small and $s_i$ is the (real) speed of machine $i$. Finally we give improved results for two machines. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Leah Epstein and Rob van Stee 2007 Is Part Of Dagstuhl Seminar Proceedings, Volume 7261, Fair Division (2007) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/DagSemProc.07261.10 urn:nbn:de:0030-drops-12427 https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07261.10 eng https://creativecommons.org/licenses/by/4.0/legalcode