In the context of local energy communities (LECs), prosumers are the main actors, as they can both produce and consume energy. Prosumers can interact with each other, and peer-to-peer (P2P) energy trading allows prosumers belonging to the same LEC to exchange energy with each other. This allows energy production to be consumed internally by the community, which has the benefits of reducing costs for energy consumption and reducing the amount of energy traveling from/to the external grid, which causes transmission losses and wears and tear to the grid itself. This paper proposes a design for the P2P market from a game-theoretical point of view, where prosumers are modeled as selfish agents whose goal is to maximize their own profits in energy trading. The purposes of this market design are to (i) discourage prosumers from curtailing their own energy production, (ii) avoid congestions as much as possible, (iii) encourage self-consumption from prosumers, and (iv) guarantee that the selfish behavior of prosumers allows for a common strategy. Furthermore, this work considers the possibility of prosumers making coalitions between themselves, and show how this still allows for the existence of a common strategy. Simulations of the proposed market design have been run on data from a grid in Cardiff, UK, and show how the proposed mechanism allows for cost reduction and encourages energy self-consumption. Experiments results show that the system discourages the formation of small coalitions, and encourages instead cooperation from all the prosumers in the community.