Quality of routing congestion games in wireless sensor networks

We consider congestion games in wireless sensor networks that offer quantitatively distinct classes of routing paths. Each routing class is characterized by a service cost. Within a routing class, the maximum link congestion is also an important metric for measuring the quality of the paths. Here, we study routing games where each player i selfishly selects a path with a respective routing class that simultaneously minimizes its maximum edge congestion Ci and service cost Si, in other words minimizes Ci + Si. We examine the quality of Nash-equilibria and prove that the price of stability is 1. The price of anarchy is bounded above by min(C, S) · m log n, where m is the number of routing classes, n is the size of the graph, and C* and S* are the optimal coordinated congestion and service costs. Thus, under certain circumstances, the player's selfishness does not hurt the social welfare and actually the equilibria can give good approximations for the coordinated optimal social cost.