“…Weighted congestion games are among the core topics in the game theory, operations research, computer science, and economics literature. This class of games has several applications such as scheduling games, routing games, facility location games, network design games, etc; see Ackermann et al [1], Anshelevich et al [5], Chen and Roughgarden [11], Gairing et al [18], Ieong et al [23], and Milchtaich [27]. In all of the above applications there are two fundamental goals from a system design perspective: (i) the system must be stabilizable, that is, there must exist a stable point (PNE) from which no player wants to unilaterally deviate; (ii) myopic play of the players should guide the system to a stable state.…”