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Network slicing to enable resource sharing among multiple tenants-network operators and/or services-is considered as a key functionality for next generation mobile networks. This paper provides an analysis of a well-known model for resource sharing, the share-constrained proportional allocation mechanism, to realize network slicing. This mechanism enables tenants to reap the performance benefits of sharing, while retaining the ability to customize their own users' allocation. This results in a network slicing game in which each tenant reacts to the user allocations of the other tenants so as to maximize its own utility. We show that, for elastic traffic, the game associated with such strategic behavior converges to a Nash equilibrium. At the Nash equilibrium, a tenant always achieves the same or better performance than that of a static partitioning of resources, thus providing the same level of protection as static partitioning. We further analyze the efficiency and fairness of the resulting allocations, providing tight bounds for the price of anarchy and envy-freeness. Our analysis and extensive simulation results confirm that the mechanism provides a comprehensive practical solution to realize network slicing. Our theoretical results also fills a gap in the analysis of this resource allocation model under strategic players.