The efficiency analysis for oligopolistic games when cost functions are non-separable

By deriving an upper bound of the so-called 'price of anarchy', this paper analyses the efficiency of oligopolistic games in networks with non-separable and asymmetric cost functions, splittable flows and fixed demands. The new bound is determined by the optimal objective function values of some optimisation problems. In particular, for some special cases, the bound turns out to be explicit in the sense that it is representable explicitly by the number of players, and the constants measuring the degree of asymmetry and non-linearity of the cost function.