Shared parking firms offer a double-sided platform for parking space sharing. Many of these firms provide differentiated service levels to both suppliers and buyers. This new phenomenon in the parking industry materialized thanks to recent innovations in IoT-enabled automation and electric vehicle charging technologies. We study shared parking firms. Specifically, we formulate the firm's location and quality decision problem by using a multiplicative interaction model with competition. A non-cooperative game renders the optimized quality levels and location selections at Nash equilibrium in the presence of competition. We illustrate managerial insights with a small-sized problem. For industry practitioners, we propose a tailored branch and bound based exact algorithm and a problem-specific genetic algorithm for large-sized problems. Simulated computational results confirm the effectiveness and efficiency of the proposed shared-parking decision support model.