The local energy market (LEM) has recently been introduced to facilitate peer-to-peer (P2P) energy trading within an integrated energy market. Nevertheless, sharing energy can result in profit loss for participants, reducing their incentive to join the coalition. This chapter introduces a trading mechanism for the market organizer to allocate cooperative surplus based on the market contribution of each participant. This model ensures key market mechanism attributes: social welfare maximization, individual rationality, cost recovery, and incentive compatibility, allowing participants to receive their fair share and avoid profit reductions. Additionally, the unpredictable and intermittent nature of power outputs from distributed renewable energy sources presents a significant challenge for organizing a LEM. Thus, an adaptive robust optimization (ARO) algorithm is used to identify scenarios that enhance conservativeness and economy, improving the efficiency of the market-clearing process. We transform the original problem into a tri-level model and solve it through iterative internal and external formulations. Numerical results demonstrate a social welfare increase of $2751 compared to the independent mode, with a 71.55% improvement in calculation efficiency using the ARO algorithm.