The energy sector is undergoing a transformative shift, driven by advancements in Distributed Energy Resources (DERs), the digitization of the energy supply chain and decarbonization policy objectives across the world. This paradigm shift has led to the emergence of Local Energy Markets (LEMs), which enable small-scale prosumers to actively participate in the energy market, trade power, and leverage their flexible resources. To ensure the success and acceptance of LEMs, this paper proposes a cooperative game-theoretic approach that fosters prosumer engagement and fair profit allocation. We utilize prospect theory from behavioural economics to examine the decision-making process of prosumers and incorporate their preferences for changes in wealth status. By adopting a cooperative game structure, prosumers can pool their resources, reduce transaction costs, and enhance data utilization. The paper introduces a novel pricing algorithm inspired by prospect theory that incentivizes prosumer participation and accounts for the uncertainty involved in LEM operations. Additionally, a computationally efficient method for profit allocation based on the variation of the Shapley value is proposed to ensure scheme stability. A use case evaluation is conducted on a real-world low-voltage network, demonstrating the effectiveness of the proposed approach in terms of economic efficiency and market characteristics. The results highlight the benefits of the consumer-centric LEM, including improved local trading dynamics, fair profit distribution, and enhanced grid stability. Overall, this research contributes to the design and development of LEMs that prioritize prosumer engagement, community cooperation, financial inclusion and democratization of the energy market.