"Cloud Kitchens" are delivery-only facilities that house multiple restaurants. Food-delivery platforms operate such kitchens to exploit two advantages: (i) Location advantage, arising due to a cloud-kitchen's central location this enables lower delivery times to customers. (ii) Consolidation advantage, which accrues when multiple restaurants choose to co-locate at the cloud kitchen -- this enables the platform to use a common pool of delivery drivers, thereby reducing costs. The cloud kitchen's eventual impacts on both the restaurants and the platform are intricately connected through their respective decisions - namely, the restaurants' location decisions and the platform's chosen delivery capacity and delivery time. We examine conditions under which a cloud kitchen simultaneously benefits the primary stakeholders: delivery platform, restaurants, and customers.Our game-theoretic analysis considers two restaurants and a delivery platform. The restaurants simultaneously decide whether to stay at their initial (extreme) locations or relocate to a centrally-located cloud kitchen. The platform decides the driver headcount and the delivery times for customers. Since drivers have a carry-limit and a restaurant's delivery time to a customer depends on the customer's distance, the platform's objective is non-linear and non-convex in its decisions. We derive the platform's optimal solution by exploiting structural properties of this solution. In line with industry trends, we show that as population density increases beyond a threshold, the restaurants co-locating at the cloud kitchen is first a Pareto-dominant equilibrium and then the unique equilibrium. The platform and customers also prefer this equilibrium, leading to a win-win-win for the stakeholders.The three primary stakeholders can simultaneously benefit from a cloud-kitchen's advantages if and only if the restaurants choose to co-locate at the cloud kitchen. In turn, this co-location occurs when the population density is sufficiently high, ensuring that the cloud-kitchen's location and consolidation advantages are substantial. A cloud-kitchen's benefit to the platform further increases as drivers' operational environment becomes more constrained, i.e., drivers' carry-limit and speed decrease, and driver cost increases.