The deployment of distributed energy resources, combined with a more proactive demand side, is inducing a new paradigm in power system operation and electricity markets. Within a consumer-centric market framework, peer-to-peer approaches have gained substantial interest. Peer-to-peer markets rely on multi-bilateral direct negotiation among all players to match supply and demand, and with product differentiation. These markets can yield a complete mapping of exchanges onto the grid, hence allowing to rethink our approach to sharing costs related to usage of common infrastructure and services. We propose here to attribute such costs in a number of alternative ways that reflects different views on usage of the grid and on cost allocation, i.e., uniformly and based on the electrical distance between players. Since attribution mechanisms are defined in an exogenous manner and made transparent they eventually affect the trades of the market participants and related grid usage. The interest of our approach is illustrated on a test case using the IEEE 39 bus test system, underlying the impact of attribution mechanisms on trades and grid usage.