This paper provides a detailed description of market properties for a competitive LEM that is cleared using the SMP, VCG, and PAB approaches. We show that the proposed compensation mechanisms effectively enforce predefined fairness policies and derive exact payments for each peer depending on market results and individual peer characteristics. The case study uses real-world data to illustrate that different compensation mechanisms can be used to incentivize desirable peer behavior, e.g., installation of new distributed energy resources, investment in grid supportive generation, or flexible energy usage.