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Metaverse has recently attracted much attention from both academia andindustry. Virtual services, ranging from virtual driver training to onlineroute optimization for smart goods delivery, are emerging in the Metaverse. Tomake the human experience of virtual life more real, digital twins (DTs),namely digital replicas of physical objects, are key enablers. However, DTstatus may not always accurately reflect that of its real-world twin becausethe latter may be subject to changes with time. As such, it is necessary tosynchronize a DT with its physical counterpart to ensure that its status isaccurate for virtual businesses in the Metaverse. In this paper, we propose adynamic hierarchical framework in which a group of IoT devices is incentivizedto sense and collect physical objects' status information collectively so as toassists virtual service providers (VSPs) in synchronizing DTs. Based on thecollected sensing data and the value decay rate of the DTs, the VSPs candetermine synchronization intensities to maximize their payoffs. In ourproposed dynamic hierarchical framework, the lower-level evolutionary gamecaptures the VSPs selection by the IoT device population, and the upper-leveldifferential game captures the VSPs payoffs, which are affected by thesynchronization strategy, IoT devices selections, and the DTs value status,given VSPs are simultaneous decision makers. We further consider the case inwhich some VSPs are first movers and extend it as a Stackelberg differentialgame. We theoretically and experimentally show that the equilibrium to thelower-level game exists and is evolutionarily robust, and provide a sensitivityanalysis with respect to various system parameters. Experiments show that theproposed dynamic hierarchical game outperform the baseline.

A Dynamic Hierarchical Framework for IoT-assisted Metaverse Synchronization