The Price of Anarchy for Selfish Ring Routing is Two
  We analyze the network congestion game with atomic players, asymmetric strategies, and the maximum latency among all players as social cost. This important social cost function is much less understood than the average latency. We show that the price of anarchy is at most two, when the network is a ring and the link latencies are linear. Our bound is tight. This is the first sharp bound for the maximum latency objective. 
Xujin Chen, Benjamin Doerr, Xiaodong Hu, Weidong Ma, Rob van Stee,   Carola Winzen
cs.GT