On the price of anarchy for non-atomic congestion games under asymmetric cost maps and elastic demands

We derive several bounds for the price of anarchy of the noncooperative congestion games with elastic demands and asymmetric linear or nonlinear cost functions. The bounds established depend on a constant from the cost functions as well as the ratio between user benefit and social surplus at Nash equilibrium. The results can be viewed a generalization of that of Chau and Sim [C.K. Chau, K.M. Sim, The price of anarchy for non-atomic congestion games with symmetric cost maps and elastic demands, Operations Research Letters 31 (2003) 327–334] for the symmetric case, or a generalization of Perakis [G. Perakis, The price of anarchy when costs are nonseparable and asymmetric, Lecture Notes in Computer Science 3064 (2004) 46–58] to the elastic demand.