As defined by Aumann in 1959, a strong equilibrium is a Nash equilibrium that is resilient to deviations by coalitions. We give tight bounds on the strong price of anarchy for load balancing on related machines. We also give tight bounds for $k$-strong equilibria, where the size of a deviating coalition is at most $k$, for unrelated machines.
@InProceedings{fiat_et_al:DagSemProc.07261.12, author = {Fiat, Amos and Levy, Meital and Kaplan, Haim and Olonetsky, Svetlana}, title = {{Strong Price of Anarchy for Machine Load Balancing}}, booktitle = {Fair Division}, pages = {1--19}, series = {Dagstuhl Seminar Proceedings (DagSemProc)}, ISSN = {1862-4405}, year = {2007}, volume = {7261}, editor = {Steven Brams and Kirk Pruhs and Gerhard Woeginger}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07261.12}, URN = {urn:nbn:de:0030-drops-12256}, doi = {10.4230/DagSemProc.07261.12}, annote = {Keywords: Game theory, Strong Nash equilibria, Load balancing, Price of Anarchy} }
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