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The Internet is a hierarchical architecture comprising heterogeneous entities of privately owned infrastructures, where higher level Internet service providers (ISPs) supply connectivity to the local ISPs and charge the local ISPs for the transit services. One of the challenging problems facing service providers today is how the profitability can be increased while maintaining good service qualities as the network scales up. In this work, we seek to understand the fundamental issues on the "interplay" (or interaction) between ISPs at different tiers. Although the local ISPs (which we term peers) can communicate with each other by purchasing the connectivity from transit ISPs, there stands an opportunity for them to set up private peering relationships. Under this competitive framework, we explore the issues on 1) the impact of peering relationship; 2) resource distribution; 3) revenue maximization; and 4) condition for network upgrade. First, a generalized model is presented to characterize the behaviors of peers and the transit ISP, in which their economic interests are reflected. We study how a peer can distributively determine its optimal peering strategy. Furthermore, we show how a transit ISP is able to utilize the available information to infer its optimal pricing strategy, under which a revenue maximization is achieved. Two distributed algorithms are proposed to help ISPs to provide a fair and efficient bandwidth allocation to peers, avoiding a resource monopolization of the market. Last, we investigate the above issues in a "many-peers region," that is, when we scale up the network. We provide insightful evidence to show that the ISPs can still gain profits as they upgrade the network infrastructures. Extensive simulations are carried out to support our theoretical claims.