With a formulated game of non-cooperative internet service providers (ISPs), this paper proposes a new framework for apportioning ISP’s responsibility in an end-to-end quality of service (QoS) request. The strategy is based on Path-Classification scheme under Nash equilibrium (PC-Nash), which is obtained by classifying paths according to the quantized QoS level. Optimal QoS-level selection of individual ISP is then captured by the Nash equilibrium. To facilitate the game solution searching, a loss network model is derived for the call acceptance probabilities and the expected utility values. Solutions provided by PC-Nash are compared with three conventional policies, i.e. mosteffort (ME), least-effort (LE) and equal-distribution (ED). The reported results show the conformity of call acceptance probabilities between mathematical analysis and discrete-event simulations. Furthermore, with the utility functions of practical service models, ME and LE are found to provide comparable utilities to PC-Nash with respect to peer and retail/wholesale service models, respectively, for a network with the same path quality. However, for networks with different path qualities, PCNash outperforms all the conventional policies significantly. From this evidence, PC-Nash is thus expected to be useful in QoS provisioning of practical inter-domain networks.