Interest in sustainability has increased the share of variable renewable energy sources (VRES) in power generation. Energy storage systems' potential to mitigate intermittencies from non-dispatchable VRES has enhanced their appeal. However, the impacts of storage vary based on the owner and market conditions. We examine the policy implications of investments in utility-scale battery storage via a bi-level optimization model. The lower level depicts power system operations, modeled as either perfect competition or Cournot oligopoly to allow for the assessment of producer market power. The upper-level investor is either a welfare-maximizer or a profit-maximizing standalone merchant to reflect either welfare enhancement or arbitrage, respectively. We implement a realistic case study for Western Europe based on all possible size-location storage investment combinations. We find that market competition affects investment sizes, locations, and their profitability more than the investor's objectives. A welfare-maximizer under perfect competition invests the most in storage capacity. Consumers typically gain most from storage investments in all cases, exceeding the gains for the investors. Specifically, our results show that storage investments may either not occur or be located differently than at social optimum, if market power is exerted. Thus, policy makers need to anticipate producer market power when setting regulation.