Peer to Peer (P2P) Energy trading in a lower voltage distribution system is one of the effective approaches to increase renewable energy penetration from decentralized generators (DG). In this paper, an energy auction is proposed as a marketplace and mechanism of the market design is established to ensure a fair and efficient bidding in the auction. An optimal bidding strategy is very important to the energy auction. To solve this problem, the Bayesian Game Theory is adopted as the strategy in the energy auction to enable efficient and cost-effective bidding for each buyer. This paper proposes a procedure for the energy auction to ensure that the power losses are within acceptable range. An algorithm to transform the power loss issue to become part of bidding strategy of Bayesian Game Theory. The proposed method is showed that it has maximized the utility for prosumer on a typical distribution network.