  Metaverse as the next-generation Internet provides users with
physical-virtual world interactions. To improve the quality of immersive
experience, users access to Metaverse service providers (MSPs) and purchase
bandwidth resource to reduce the communication latency of the Metaverse
services. The MSPs decide selling price of the bandwidth resource to maximize
the revenue. This leads to a joint user association and resource pricing
problem between all users and MSPs. To tackle the problem, we formulate a
Stackelberg game where the MSPs are game leaders and users are game followers.
We resolve the Stackelberg equilibrium via the distributed and centralized
approaches, according to different privacy requirements. In the distributed
approach, the MSPs compete against each other to maximize the individual
revenue, and a user selects an MSP in a probabilistic manner. The Stackelberg
equilibrium is achieved in a privacy-friendly way. In the centralized approach,
all MSPs and users accept the unified management and their strategies are
instructed. The centralized approach acquires the superior decision-making
performance but sacrifices the privacy of the game players. Finally, we provide
numerical results to demonstrate the effectiveness and efficiency of our
schemes.
