The ever-increasing uptake of distributed energy resources necessitates the introduction of local electricity markets at the residential level. Electric retailers, who are adversely affected by these changes, can make a profit by operating local trading platforms and offering services through community-level battery storage. In this work, we propose a Stackelberg game-based approach for sizing the centralized battery unit under the operation of a multi-interval local market. The optimization is formulated as a bilevel program, where the leader is the market aggregator responsible for determining the local prices and battery charging/discharging schedules. Also, the followers in the bilevel program are prosumers, who can vary electricity consumption with respect to their comfort and cost of electricity. Upon obtaining the optimal capacity of the community storage, we modify the algorithm to efficiently operate the battery on a daily basis. The applicability of the proposed model is evaluated using real-world data of residential prosumers with rooftop photovoltaic systems for two different pricing schemes, which represents the profit trade-off between the aggregator and prosumers. The results show the profitability of the proposed model for community storage installation, where a relatively short payback period can be achieved via either pricing scheme.