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In peer-to-peer networks, nodes can be both resource providers and resource consumers at the same time. In this sense, the services offered by a peer-to-peer network rely on resource sharing among peers. This work focuses on how peers share their access link capacity between upload and download rates. In our model peers are rational agents, and choose their strategy in order to maximize their own utility. We suppose that the bottleneck is not in the network core, but in the network edge: the access link capacity of each peer connected to the network is a scarce resource and the peers have to compete for it. Instead of trying to settle the controversies which can arise, we imagine that every peer organizes an auction to give away its bandwidth. While the service rate is always granted to the peer who makes the lowest request, the amount of allocated rate depends on the implemented auction mechanism. Numerical experiments show that in a peer-to-peer game where the access link capacities are homogeneous, a second-price auction guarantees that the equilibrium rate allocation is optimal.