Mobile edge computing seeks to provide resources to different delay-sensitive applications. This is a challenging problem as an edge cloud-service provider may not have sufficient resources to satisfy all resource requests. Furthermore, allocating available resources optimally to different applications is also challenging. Resource sharing among different edge cloud-service providers can address the aforementioned limitation as certain service providers may have resources available that can be “rented” by other service providers. However, edge cloud service providers can have different objectives or utilities . Therefore, there is a need for an efficient and effective mechanism to share resources among service providers, while considering the different objectives of various providers. We model resource sharing as a multi-objective optimization problem and present a solution framework based on Cooperative Game Theory (CGT). We consider the strategy where each service provider allocates resources to its native applications first and shares the remaining resources with applications from other service providers. We prove that for a monotonic, non-decreasing utility function, the game is canonical and convex. Hence, the core is not empty and the grand coalition is stable. We propose two algorithms, Game-theoretic Pareto optimal allocation (GPOA) and Polyandrous-Polygamous Matching based Pareto Optimal Allocation (PPMPOA) that provide allocations from the core. Hence the obtained allocations are Pareto optimal and the grand coalition of all the service providers is stable. Experimental results confirm that our proposed resource sharing framework improves utilities of edge cloud-service providers and application request satisfaction.