We consider mechanisms without payments for the problem of scheduling unrelated machines. Specifically, we consider truthful in expectation randomized mechanisms under the assumption that a machine (player) is bound by its reports: when a machine lies and reports valuet i j for a task instead of the actual one t i j , it will execute for timet i j if it gets the task (unless the declared valuet i j is less than the actual value t i j , in which case, it will execute for time t i j ). Our main technical result is an optimal mechanism for one task and n players which has approximation ratio (n + 1)/2. We also provide a matching lower bound, showing that no other truthful mechanism can achieve a better approximation ratio. This immediately gives an approximation ratio of (n + 1)/2 and n(n + 1)/2 for social cost and makespan minimization, respectively, for any number of tasks. We also study the price of anarchy of natural algorithms.
The mechanism presented in REF has a tight approximation ratio bound of n+1 2 for the single-task setting; by running the mechanism independently on multiple tasks a tight bound of n+1 2
Scheduling without payments
SAGT
Computer Science