Inefficiency of Nash equilibria with parallel processing policy

In this paper, we revisit the coordination mechanism of parallel processing policy introduced in [L. Yu, K. She, H. Gong, C. Yu, Price of anarchy in parallel processing, Information Processing Letters 110 (8–9) (2010) 288–293]. For both the problem of minimizing makespan and the machine covering problem, we give the analysis of price of anarchy with this new mechanism. In the first problem, we point out an error in the original paper and provide a correct instance. Moreover, we show the exact PoA for identical and uniform machines. In the second problem, we obtain new results for several scheduling models.