Wireless sensor networks are evolving from single-application platforms towards an integrated infrastructure shared by multiple applications. Given the resource constraints of sensor nodes, it is important to optimize the allocation of applications to maximize the overall Quality of Monitoring (QoM). Recent solutions to this challenging application allocation problem are centralized in nature, limiting their scalability and robustness against network failures and dynamics. This paper presents a distributed game-theoretic approach to application allocation in shared sensor networks. We first transform the optimal application allocation problem to a submodular game and then develop a decentralized algorithm that only employs localized interactions among neighboring nodes. We prove that the network can converge to a pure strategy Nash equilibrium with an approximation bound of 1=2. Simulations based on three real-world datasets demonstrate that our algorithm is competitive against a state-of-the-art centralized algorithm in terms of QoM.