Metaverse enables users to communicate, collaborate and socialize with each other through their digital avatars. Due to the spatio-temporal characteristics, co-located users are served well by performing their software components in a collaborative manner such that a Metaverse service provider (MSP) eliminates redundant data transmission and processing, ultimately reducing the total energy consumption. The energyefficient service provision is crucial for enabling the green and sustainable Metaverse. In this article, we take an augmented reality (AR) application as an example to achieve this goal. Moreover, we study an economic issue on how the users reserve offloading services from the MSP and how the MSP determines an optimal charging price since each user is rational to decide whether to accept the offloading service by taking into account the monetary cost. A single-leader multi-follower Stackelberg game is formulated between the MSP and users while each user optimizes an offloading probability to minimize the weighted sum of time, energy consumption and monetary cost. Numerical results show that our scheme achieves energy savings and satisfies individual rationality simultaneously compared with the conventional schemes. Finally, we identify and discuss open directions on how several emerging technologies are combined with the sustainable green Metaverse.

翻译：元宇宙使用户能够通过其数字化身进行沟通、协作和社交。由于时空特性，共址用户通过协同执行其软件组件可以获得良好服务，使元宇宙服务提供商（MSP）消除冗余数据传输和处理，最终降低总能耗。节能服务提供对于实现绿色可持续的元宇宙至关重要。本文以增强现实（AR）应用为例实现这一目标。此外，我们研究了一个经济问题：用户如何向MSP预留卸载服务，以及MSP如何确定最优收费价格——因为每个理性用户会根据货币成本决定是否接受卸载服务。在MSP与用户之间构建了单领导者多追随者的Stackelberg博弈，每个用户通过优化卸载概率来最小化时间、能耗和货币成本的加权和。数值结果表明，与传统方案相比，我们的方案在实现节能的同时满足个体理性。最后，我们识别并讨论了若干新兴技术与可持续绿色元宇宙相结合的未来发展方向。