World Wide Web

Service (business)

Interoperability

Economics

Computer science

Virtual reality

Distributed computing

Computer network

Stackelberg competition

Mathematics

Metaverse

Synchronization (alternating current)

Mathematical economics

Economy

Channel (broadcasting)

Human–computer interaction

IEEE Internet of Things Journal

Metaverse, also known as the Internet of 3-D worlds, has recently attracted much attention from both academia and industry. Each virtual subworld, operated by a virtual service provider (VSP), provides a type of virtual service. Digital twins (DTs), namely, digital replicas of physical objects, are key enablers. Generally, a DT belongs to the party that develops it and establishes the communication link between the two worlds. However, in an interoperable metaverse, data-like DTs can be “shared” within the platform. Therefore, one set of DTs can be leveraged by multiple VSPs. As the quality of the shared DTs may not always be satisfying, in this article, we propose an agile solution, i.e., a dynamic hierarchical framework, in which a group of Internet of Things devices in the lower level are incentivized to collectively sense physical objects’ status information and VSPs in the upper level determine synchronization intensities to maximize their payoffs. We adopt an evolutionary game approach to model the devices VSP selections and a simultaneous differential game to model the optimal synchronization intensity control problem. We further extend it as a Stackelberg differential game by considering some VSPs to be first movers. We provide open-loop solutions based on the control theory for both formulations. We theoretically and experimentally show the existence, uniqueness, and stability of the equilibrium to the lower level game and further provide a sensitivity analysis for various system parameters. Experiments show that the proposed dynamic hierarchical game outperforms the baseline.

A Dynamic Hierarchical Framework for IoT-Assisted Digital Twin Synchronization in the Metaverse