MoTS: Decentralized Model Trading & Sharing

• MoTS is a framework for decentralized model and resource trading among autonomous agents using incentive-compatible and privacy-preserving mechanisms with multi-dimensional metrics like Immersion-of-Model.
• It employs equilibrium-based incentive strategies, including Stackelberg games and Nash bargaining, to align contributions and optimize resource allocation across metaverse and microgrid domains.
• MoTS integrates distributed algorithms such as deep reinforcement learning and ADMM to achieve notable performance improvements in training time and cost reduction under dynamic operational constraints.

Model Trading and Sharing (MoTS) refers to a class of frameworks and algorithms for the decentralized exchange and allocation of models or resources across autonomous agents—such as metaverse users (MUs) and service providers (MSPs) or interconnected microgrids—using incentive-compatible, privacy-preserving, equilibrium-driven mechanisms. In the context of vehicular metaverse services and energy microgrid systems, MoTS addresses fundamental constraints of latency, privacy, resource heterogeneity, and incentive alignment, leveraging advanced constructs such as multi-dimensional metrics (e.g., immersion-of-model, IoM), federated learning, Stackelberg games with equilibrium constraints, Nash bargaining, and distributed algorithms including deep reinforcement learning (DRL) and consensus-based optimization.

1. Framework Overview and Entity Roles

MoTS architectures delineate participating agents as either resource owners (e.g., MSPs or microgrids) or contributors/consumers (e.g., MUs or microgrid users). MSPs broadcast global models and digital currency schedules, aggregate contributed updates, and deploy improved versions; MUs (or microgrid users) consume resources, process local data, provide updates, and receive incentives proportional to their contribution value.

The workflow consists of two primary phases:

• Phase I (Trading and Incentivization): MSPs announce prices per unit of immersion or energy; contributors solve local resource allocation subproblems; MSPs adjust prices, targeting equilibrium.
• Phase II (Aggregation/Federated Learning or Scheduling): Contributors allocate compute and bandwidth according to equilibrium outcomes, upload updates, which are aggregated using schemes such as FedAvg or executed as decentralized scheduling.

In microgrids, each trading agent manages local generation, storage, and energy trading flows, balancing supply against consumption and subject to operational constraints (Wang et al., 2016).

2. Multi-Dimensional Utility Metrics

A core element of MoTS is the quantification of contribution value through composite utility metrics. In vehicular metaverse applications, the Immersion-of-Model (IoM) metric quantifies the utility of model updates as follows:

$V_{mn} = I_{mn}\,(\tau_n - \overline{\Delta}_{mn})$

where:

• Freshness: $\tau_n - \overline{\Delta}_{mn}$, with $\overline{\Delta}_{mn}$ defined as the average age of information, analytically dependent on resource allocation and data throughput.
• Accuracy: $1/\theta_m$, where $\theta_m$ is the MU’s local training accuracy threshold.
• DataAmount: $|X_{mn}| = x_m\,\tau_n$.
• DataValue: $$\omega_{mn} = \frac{1}{|X_{mn}|} \sum_i (\hat{z}_i - z_i)^2$$ (MSE over local data).

These components are linearly combined: $$\text{IoM}(M) = \alpha\,\text{Freshness} + \beta\,\text{Accuracy} + \gamma\,\text{DataAmount} + \delta\,\text{DataValue}$$ with $\alpha, \beta, \gamma, \delta$ weighting the respective contributions (Wu et al., 2024).

In microgrid contexts, cost functions (e.g., energy procurement, comfort/discomfort, battery cycling costs) and trading flows are encapsulated in social-welfare and Nash-product metrics, informing both optimal resource scheduling and benefit-sharing (Wang et al., 2016).

3. Equilibrium-Based Incentive Mechanisms

Model/resource trading in MoTS frameworks is typically formalized as a multi-leader multi-follower equilibrium problem:

• Stackelberg Game:
  • Followers (MUs/microgrids): Solve local optimization

  $$\max_{f_{mn}, B_{mn}} \Phi_m = \sum_{n} [p_{mn} V_{mn} - C_{mn}]$$

  subject to compute and bandwidth constraints, response uniqueness guaranteed. - Leaders (MSPs): Set price schedules to maximize

  $$\max_{p_{mn} > 0} \Psi_n = \mu_n \ln(1+\sum_m V_{mn}) - \sum_m p_{mn} V_{mn}$$

  taking contributors' best-responses as constraints; admits a unique Nash equilibrium (Wu et al., 2024).

• Nash Bargaining (Microgrids): Social cost minimization yields global scheduling, and Nash bargaining splits surplus via:

  $$\max \prod_{i \in \mathcal{M}'} [\Delta_i - \sum_{j \neq i} \pi_{i,j} ]$$

subject to payment (benefit) and market-clearing constraints (Wang et al., 2016).

4. Distributed Algorithms and Privacy Preservation

MoTS emphasizes decentralized algorithms for both equilibrium computation and policy adaptation:

• Deep Reinforcement Learning (DRL): In dynamic channel conditions, MSP reward policies are modeled as multi-agent Markov Decision Processes (MAMDPs). Each MSP maintains private actor-critic networks trained by Proximal Policy Optimization (PPO), using only observed immersion scores and channel feedback, with no access to contributors' raw data, local cost parameters, or resource allocations (Wu et al., 2024).

• Distributed ADMM (Microgrids): Convex scheduling and bargaining are solved using alternating direction methods with auxiliary variable splitting and virtual clearing houses, ensuring minimal information exchange and strong privacy—no private load or cost data is disclosed (Wang et al., 2016).

5. Quantitative Performance Evaluation

Experimental setups demonstrate the efficacy of MoTS across domains:

• Vehicular Metaverse (Model Trading):

  • MNIST (ResNet-18), GTSRB (Faster R-CNN); $M=5$ MUs, $N=3$ MSPs.
  • MoTS outperforms benchmarks:
  • IoM increase: 38.3% (MNIST), 37.2% (GTSRB).
  • Training time reduction to target accuracy/mAP: up to 49.8% (GTSRB), 43.5% (MNIST).
  • Steered updates maximize immersion, accelerate convergence even under dynamic uplink/channel conditions (Wu et al., 2024).
• Microgrid Energy Trading:
  • Three microgrids, 24-hour horizon, wind and price data, operational constraints.
  • Cost reduction via trading: up to 13.2% system-wide.
  • Individual savings: up to 29.4% (MG 1).
  • Nash bargaining achieves fair surplus division; ADMM converges with low communication overhead (Wang et al., 2016).

Performance Table: MNIST, Time to Target Accuracy

Method	MSP 1	MSP 2	MSP 3
MoTS	15.23s	13.09s	7.59s
x_based	17.79s	18.03s	19.80s
w_based	>30s	24.04s	10.28s
w_x_based	23.20s	19.08s	12.34s
fixed	>30s	>30s	>30s

Performance Table: Microgrid Trading, Cost Comparison

	MG 1	MG 2	MG 3	System
No trading	243.8	607.0	787.0	1637.8
With trading	296.5	377.4	748.6	1422.4
Net gain	172.1	535.2	715.2	1422.4

6. Context, Generalization, and Implications

MoTS generalizes to settings where autonomous agents maintain local resources or models that could benefit the global system if efficiently shared or traded. By embedding multi-dimensional utility metrics and principled incentive mechanisms—while respecting privacy and autonomy—MoTS frameworks offer scalable solutions to distributed learning and resource scheduling in heterogeneous, networked environments.

A plausible implication is that future MoTS deployments may extend to other domains (e.g., federated healthcare, IoT sensor fusion) where decentralized updates, fairness in value attribution, and privacy constraints are paramount. The integration of advanced DRL and distributed optimization architectures will likely continue to be central in managing incentive-compatible trading under dynamic system conditions.