This paper studies two scheduling games on identical batching-machines with activation cost,where each game comprises n jobs being processed on m identical batching-machines.Each job,as an agent,chooses a machine(or,m...This paper studies two scheduling games on identical batching-machines with activation cost,where each game comprises n jobs being processed on m identical batching-machines.Each job,as an agent,chooses a machine(or,more accurately,a batch on a machine)for processing in order to minimize its disutility,which is comprised of its machine’s load and the activation cost it shares.Based on previous results,we present the Mixed strategy Nash Equilibria(MNE)for some special cases of the two games.For each game,we first analyze the conditions for the nonexistence of Nash equilibrium,then provide the MNE for the conditions,and offer the efficiency of MNE(mixed price of anarchy).展开更多
基金supported by the National Natural Science Foundation of China(Nos.12001313,11771386,11728104,and 62202054)the Natural Science Foundation of Shandong Province of China(No.ZR2020QA023)the Natural Sciences and Engineering Research Council of Canada(NSERC)(No.283106).
文摘This paper studies two scheduling games on identical batching-machines with activation cost,where each game comprises n jobs being processed on m identical batching-machines.Each job,as an agent,chooses a machine(or,more accurately,a batch on a machine)for processing in order to minimize its disutility,which is comprised of its machine’s load and the activation cost it shares.Based on previous results,we present the Mixed strategy Nash Equilibria(MNE)for some special cases of the two games.For each game,we first analyze the conditions for the nonexistence of Nash equilibrium,then provide the MNE for the conditions,and offer the efficiency of MNE(mixed price of anarchy).
