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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 to increase the profitability while maintaining good service qualities. In this work, we seek to understand the fundamental issues on the "interplay" (or interaction) between ISPs at different tiers. While 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 (a) impact of peering relationship, (b) resource distribution and (c) revenue maximization. Firstly, 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. A distributed algorithm is proposed to help ISPs to provide a fair and efficient bandwidth allocation to peers, avoiding a resource monopolization of the market. Extensive simulations are carried out to support our claims.