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Many studies on Internet Service Provider (ISP) interconnection make simplifying assumptions on the implementation of the service provision. Our work explicitly models the ISP service that is provided to users that run peer-to-peer applications and it analyses the behavior of competing ISPs. The ISPs have agreed to peer each other and each ISP has purchased transit service from one Internet Backbone Provider. The quality of service, the equilibrium prices and the market shares that the competition game yields are computed by means of our model. Our work assesses the strategy of an ISP which provisions its transit link against a competing ISP in terms of competitive advantage and social welfare. And it assesses the effect of the entrance of more competing ISPs.