The emergence of the Metaverse has brought forth a new era of social networks, offering immersive virtual spaces for users to engage in social activities. However, the resource-intensive nature of rendering avatars and virtual scenes places considerable strain on end devices. To improve the Quality of Experience (QoE) for users, the utilization of edge servers' resources becomes crucial. Moreover, accommodating the diverse QoE requirements and time dynamics of users (e.g., user join/departure, and social activities) escalates the complexity of resource allocation. In this paper, we propose an auction-based dynamic resource allocation algorithm to efficiently and economically allocate various limited resources (e.g., CPU, GPU, RAM, and VRAM) of edge servers to social user groups in a rapid and decentralized manner. First, with heterogeneous and dynamic varying resources at each Planet (i.e., edge server to host Metaverse users), we design an optimal Planet access scheme to help social user groups to determine which Planet to connect. Second, considering the dynamic nature of social applications, e.g., users dynamically join and depart the network with dynamic requirements on resources, we present a multi-round auction game between social user groups and edge servers to compete for the dynamic multi-dimensional resources before each scheduled time period. By using the above mechanisms, our scheme optimizes the dynamic resource utilization by considering the social feature of Metaverse. Using extensive simulations, we demonstrate that the proposed algorithm dynamically and effectively allocates resources for social Metaverse activities, outperforming conventional allocation approaches.