[Paper Review] A Dynamic Hierarchical Framework for IoT-assisted Metaverse Synchronization

Yue Han, Dusit Niyato+6 more|arXiv (Cornell University)|Mar 8, 2022

Digital Transformation in Industry23 citations

TL;DR

The paper proposes a dynamic hierarchical framework using movable IoT devices to synchronize digital twins in the Metaverse, modeled via a lower-level evolutionary game for UAV-VSP selection and upper-level differential games (simultaneous and Stackelberg) for VSP synchronization strategies, with equilibrium analyses and simulations.

ABSTRACT

Metaverse has recently attracted much attention from both academia and industry. Virtual services, ranging from virtual driver training to online route optimization for smart goods delivery, are emerging in the Metaverse. To make the human experience of virtual life more real, digital twins (DTs), namely digital replicas of physical objects, are key enablers. However, DT status may not always accurately reflect that of its real-world twin because the latter may be subject to changes with time. As such, it is necessary to synchronize a DT with its physical counterpart to ensure that its status is accurate for virtual businesses in the Metaverse. In this paper, we propose a dynamic hierarchical framework in which a group of IoT devices is incentivized to sense and collect physical objects' status information collectively so as to assists virtual service providers (VSPs) in synchronizing DTs. Based on the collected sensing data and the value decay rate of the DTs, the VSPs can determine synchronization intensities to maximize their payoffs. In our proposed dynamic hierarchical framework, the lower-level evolutionary game captures the VSPs selection by the IoT device population, and the upper-level differential game captures the VSPs payoffs, which are affected by the synchronization strategy, IoT devices selections, and the DTs value status, given VSPs are simultaneous decision makers. We further consider the case in which some VSPs are first movers and extend it as a Stackelberg differential game. We theoretically and experimentally show that the equilibrium to the lower-level game exists and is evolutionarily robust, and provide a sensitivity analysis with respect to various system parameters. Experiments show that the proposed dynamic hierarchical game outperform the baseline.

Motivation & Objective

• Motivate synchronization of digital twins (DTs) in the Metaverse to reflect changing physical states for virtual services.
• Propose a movable IoT-based data collection framework to support ad-hoc DT synchronization for diverse VSPs.
• Model UAVs’ VSP selection via an evolutionary game under bounded rationality.
• Formulate optimal VSP synchronization strategies as a simultaneous differential game and a Stackelberg differential game.
• Provide theoretical guarantees on equilibrium existence, robustness, and practical performance improvements through experiments.

Proposed method

• Model the DT value dynamics with dz_m/dt = η_m(t) - θ_m z_m(t).
• Represent UAVs choosing VSPs via an evolutionary replicator dynamics dx_m/dt = δ x_m (u_m − ū).
• Define VSP incentives R_m(t) = η_m(t) d_m g(θ_m) and UAV utility u_m = R_m/(N x_m) − c_m.
• Solve upper-level problems as open-loop Nash differential game for simultaneous decision making and as a Stackelberg differential game when leaders exist.
• Formulate the VSP objective J_m as a weighted sum of components J_m^1, J_m^2, J_m^3, J_m^4 with a Hamiltonian H_m for optimal control.
• Establish existence, uniqueness, and asymptotic stability of the lower-level equilibrium (EE) and analyze sensitivity to system parameters.

Experimental results

Research questions

• RQ1 How should VSP synchronization intensities η_m(t) be chosen to maximize VSP payoffs given DT value dynamics?
• RQ2 How do UAVs’ VSP selections evolve under bounded rationality and incentives?
• RQ3 What are the equilibrium properties (existence, uniqueness, stability) of the lower-level evolutionary game?
• RQ4 What is the performance gain of simultaneous vs Stackelberg differential games compared to static baselines?
• RQ5 How do system parameters (θ_m, d_m, c_m, etc.) affect DT values and UAV allocations?

Key findings

• The lower-level replicator dynamics admit a unique evolutionarily stable equilibrium (EE) that is asymptotically stable for a single UAV population.
• Both the simultaneous differential game and the Stackelberg differential game yield higher accumulated payoffs for VSPs than a static baseline.
• The framework captures DT value decay and data contribution dynamics, enabling VSPs to optimize synchronization intensity in a principled control-theoretic setting.
• Incentive design links synchronization rate, number of DTs, and decay rate to UAV incentives, influencing UAV distribution across VSPs.
• The hierarchical model supports ad-hoc, scalable DT synchronization via movable IoT devices, with theoretical guarantees and sensitivity analyses.