The current Internet architecture comprises of different privately owned Internet service providers (ISPs) where higher tier ISPs supply connectivity service to lower tier ISPs and charge these ISPs for the transit service. For the higher tier ISPs, the main concern is how to increase the profit by attracting more lower tier ISPs (or traffic), while the lower tier ISPs concern about the connectivity, quality of service as well as the cost of the transit service. In this work, we seek to understand the interaction between different tiers of ISPs. Note that the lower tier ISPs can transmit traffic to each other, either by purchasing the service from higher tier ISPs, or by setting "private peering links" between themselves. Higher tier ISPs, on the other hand, cannot charge the transit service at will since there is competition among higher tier ISPs. We model the interaction of these ISPs via a game theoretic approach. We study the issues of (a) impact of private peering relationship among the lower tier ISPs, (b) under a competitive market, how can the higher tier ISPs perform resource allocation and revenue maximization so that resource monopoly can be avoided, and (c) conditions wherein higher tier ISPs are willing to perform network upgrade, in particular, when we scale up the network. Our mathematical framework provides insights on the interaction among ISPs and shows these ISPs can still gain profits as they upgrade the network infrastructures. Extensive simulations are carried out to quantify and support our theoretical claims.