Communication functionality is described for conducting communication among a plurality of participants in peer-to-peer fashion. The communication functionality comprises peer-to-peer overlay functionality configured to establish a peer-to-peer overlay network that includes a plurality of participants. The peer-to-peer overlay functionality relies on endpoint provider functionality for physically exchanging information among the plurality of participants in the peer-to-peer overlay network. The endpoint provider functionality exchanges information using a transport mechanism. The transport mechanism accommodates multiple different transport protocols for exchanging information among the plurality of participants, allowing different pairs of participants to communicate with each other using different respective transport protocols. Address translation functionality is employed for translating address information between a first address space used by the peer-to-peer overlay functionality and a second address space used by the endpoint provider functionality.