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We study fair content allocation strategies in caching networks through a utility-driven framework, where each request achieves a utility of its caching gain rate. The resulting problem is NP-hard. Submodularity allows us to devise a deterministic allocation strategy with an optimality guarantee factor arbitrarily close to 1-1/e. When 0 < α ≤ 1, we further propose a randomized strategy that attains an improved optimality guarantee, (1 - 1/e)1-α, in expectation. Through extensive simulations over synthetic and real-world network topologies, we evaluate the performance of our proposed strategies and discuss the effect of fairness.