Metaverse is the fusion of physical and virtual world, where Metaverse users (MUs) interact with both physical and virtual world in real-time. To improve the Quality of Experience (QoE) of the MUs, it is essential to feed the whole Metaverse system with high quality real-world data such as higher sampling rate and bit rate to create better and up-to-date replication of the physical world i.e., digital (or mirror) world. On the other hand, the owner of the smart Internet of Things (IoT) devices or sensors that collect data from the real-world on behalf of the Metaverse systems should be well paid for collecting such high quality data. Therefore, in this work, to maintain the balance between the required quality of data, and the profit and cost associated with such data collection in Metaverse systems, we design a Distributed and Dynamic Reputation based Resource Allocation (D2R2) model. This D2R2 model leads the rational smart devices to feed the Metaverse systems with high quality data by maintaining its reputation while earning higher payoffs. To find the optimal solution of the proposed D2R2 model, we first fit the D2R2 into the Stackelberg gaming model, and then prove that proposed D2R2 model have Stackelberg Equilibrium point. Later, we use Alternating Direction Method of Multipliers (ADMM) algorithm for its faster convergence to find the optimal solutions of the Stackelberg gaming model in a distributed manner. Finally, we implement the proposed D2R2 model in MATLAB and provide numerical results to demonstrate the effectiveness and efficiency of the proposed model.