Joining Edge-Enabled Metaverse Services with Network Externality: A Stackelberg Game Approach.

The metaverse is defined as a three-dimensional virtual-real fusion network focused on social connection. Edge computing can empower the metaverse by providing computing resources to realize real-time motion tracking, visual or auditory rendering and virtual scene dynamic change at the edge of networks. Users enjoy the immersive experience provided by the Metaverse Service Provider (MSP), and interact through digital avatars in the virtual world by requesting metaverse services. In this paper, we formulate the edge computing resources pricing, metaverse service rendering bitrate pricing and request problem in the metaverse. Especially, we model the interactions among edge servers, the MSP and Metaverse Service Users (MSUs) as a hierarchical three-stage Stackelberg game. The problem of joining edge-enabled metaverse services is also studied with the consideration of network externality, including the network effect and congestion effect. Based on the backward induction method, we derive the optimal computing resources pricing of edge servers, rendering bitrate pricing of the MSP, and rendering bitrate requests of MSUs. We also prove the existence and uniqueness of the Stackelberg game equilibrium. Simulation results show that the network effect can bring more positive utilities to entities when the social tie coefficient among MSUs is higher. Besides, all entities in the edge-enabled metaverse are affected negatively by the congestion effect.