•A motivational psychology framework is introduced for peer-to-peer energy trading.•A game theoretic design for peer-to-peer energy trading is demonstrated.•An up-to-date literature review of peer-to-peer energy trading schemes is provided. Peer-to-peer trading in energy networks is expected to be exclusively conducted by the prosumers of the network with negligible influence from the grid. This raises the critical question: how can enough prosumers be encouraged to participate in peer-to-peer trading so as to make its operation sustainable and beneficial to the overall electricity network? To this end, this paper proposes how a motivational psychology framework can be used effectively to design peer-to-peer energy trading to increase user participation. To do so, first, the state-of-the-art of peer-to-peer energy trading literature is discussed by following a systematic classification, and gaps in existing studies are identified. Second, a motivation psychology framework is introduced, which consists of a number of motivational models that a prosumer needs to satisfy before being convinced to participate in energy trading. Third, a game-theoretic peer-to-peer energy trading scheme is developed, its relevant properties are studied, and it is shown that the coalition among different prosumers is a stable coalition. Fourth, through numerical case studies, it is shown that the proposed model can reduce carbon emissions by 18.38% and 9.82% in a single day in Summer and Winter respectively compared to a feed-in-tariff scheme. The proposed scheme is also shown to reduce the cost of energy up to 118 ¢ and 87 ¢ per day in Summer and Winter respectively. Finally, how the outcomes of the scheme satisfy all the motivational psychology models is discussed, which subsequently shows its potential to attract users to participate in energy trading.