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
This paper studies scheduling games with potential penalties on the move of jobs.There are a set of machines and a set of jobs.Each job could choose one machine and be processed by the chosen one.Jobs that try to chan...This paper studies scheduling games with potential penalties on the move of jobs.There are a set of machines and a set of jobs.Each job could choose one machine and be processed by the chosen one.Jobs that try to change their original choice will incur additional costs,which is proportional to its processing time with proportional parameter δ≥0.A schedule is a δ-NE if no job has the incentive to change its choice unilaterally.The δ-NE is a generation of Nash equilibrium,and its inefficiency can be measured by the δ-PoA,which is also a generalization of the Price of Anarchy.For the game with the social cost of minimizing the makespan,the exact δ-PoA for any number of machines and any δ≥0 is obtained.For the game with the social cost of maximizing the minimum machine load,an upper bound on the δ-PoA is presented,and tight bounds are given for 2≤m≤11 and any δ≥0,where m is the number of machines.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).
基金supported by the National Natural Science Foundation of China(No.12071427).
文摘This paper studies scheduling games with potential penalties on the move of jobs.There are a set of machines and a set of jobs.Each job could choose one machine and be processed by the chosen one.Jobs that try to change their original choice will incur additional costs,which is proportional to its processing time with proportional parameter δ≥0.A schedule is a δ-NE if no job has the incentive to change its choice unilaterally.The δ-NE is a generation of Nash equilibrium,and its inefficiency can be measured by the δ-PoA,which is also a generalization of the Price of Anarchy.For the game with the social cost of minimizing the makespan,the exact δ-PoA for any number of machines and any δ≥0 is obtained.For the game with the social cost of maximizing the minimum machine load,an upper bound on the δ-PoA is presented,and tight bounds are given for 2≤m≤11 and any δ≥0,where m is the number of machines.
