On the balancedness of multiple machine sequencing games |
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| Institution: | 1. Instituto de Matemáticas, Universidad Nacional Autonóma de México, Campus Juriquilla, Querétaro, Mexico;2. Department of Geometry and MTA-ELTE GAC Research Group, Eötvös Loránd University, 1117 Budapest, Pázmány s. 1/c, Hungary;3. UMDI-Facultad de Ciencias, Universidad Nacional Autonóma de México, Campus Juriquilla, Querétaro, Mexico;1. Dorodnicyn Computing Centre, FRC CSC RAS, 40, Vavilova, Moscow 119333, Russia;2. Moscow Institute of Physics and Technology, 9, Institutskiy per., Dolgoprudny, Moscow region 141701, Russia;1. College of Life Sciences and Laboratory for Marine Biology and Biotechnology of Qingdao National Laboratory for Marine Science and Technology, Zhejiang University, Hangzhou 310058, The People’s Republic of China;1. Department of Statistics, Feng Chia University, Taichung, Taiwan, ROC;2. Department of Computer Science and Information Management, Hungkuang University, Sha Lu, Taiwan, ROC |
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| Abstract: | This paper takes a game theoretical approach to sequencing situations with m parallel and identical machines. We show that in a cooperative environment cooperative m-sequencing games, which involve n players, give rise to m-machine games, which involve m players. Here, n corresponds to the number of jobs in an m-sequencing situation, and m corresponds to the number of machines in the same m-sequencing situation. We prove that an m-sequencing game is balanced if and only if the corresponding m-machine game is balanced. Furthermore, it is shown that m-sequencing games are balanced if m∈{1,2}. Finally, if m⩾3, balancedness is established for two special classes of m-sequencing games. Furthermore, we consider a special class of m-sequencing situations in a noncooperative setting and show that a transfer payments scheme exists that is both incentive compatible and budget balanced. |
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