Lower Bound for Envy-Free and Truthful Makespan Approximation on Related Machines
A deterministic envy-free, truthful, individually rational, and anonymous mechanism cannot approximate the makespan strictly better than 2 − 1/m, where m is the number of machines. This result contrasts with prior work giving a deterministic PTAS for envy-free anonymous assignment and a distinct deterministic PTAS for truthful anonymous mechanism.
For two machines of different speeds, the unique deterministic scalable allocation of any envy-free, truthful, individually rational, and anonymous mechanism is to allocate all jobs to the quickest machine. This allocation is the same as that of the VCG mechanism, yielding a 2-approximation to the minimum makespan.
No payments can make any of the prior published monotone and locally efficient allocations that yield better than an m-approximation for Q||Cmax [1,3,5,9,13] a truthful, envy-free, individually rational, and anonymous mechanism.
KeywordsMechanism Design Incentive Compatible Envy-Free Makespan Approximation
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