Asynchronous Federated Learning (AFL) is acclaimed for accelerating collaborative training on heterogeneous systems by eliminating the wait for stragglers. While current solutions focus on improving convergence amidst update delays, they neglect how delayed aggregation fosters free-riding attacks, allowing malicious clients to easily extract the global model without contribution. This behavior results in significant fairness issues and performance degradation. To address this challenge, we propose OPTION, the first online pricing strategy tailored to mitigate free-riding in AFL. OPTION establishes an economic model in which access to model updates is purchased using credits earned from verified contributions. Specifically, OPTION values each model update according to its marginal performance gain and training cost, and subsequently necessitates a download fee from each client based on the Hotelling model to prevent zero-cost acquisition. Moreover, OPTION rewards clients for successful updates under non-arbitrage constraints, effectively balancing individual utility and task budget. To maximize the average model performance while satisfying these conditions, OPTION leverages the Lyapunov drift framework and a probabilistic sampling-based algorithm to optimize the pricing parameters. Extensive experimental results on three real-world datasets demonstrate that OPTION effectively mitigates freeriding attacks in AFL, increases the number of valid updates by at least 23.97%, and achieves a model accuracy improvement of at least 3.01% compared to state-of-the-art baselines.

Federated learning (FL) facilitates privacy-preserving collaborative intelligence, making it ideal for mobile edge computing (MEC)-enabled Industrial Internet of Thing (IIoT). However, the autonomy of participants leads to unstable edge associations, hampering FL deployment. Existing studies typically prioritize device incentives but overlook price competition and network congestion at the server level. To tackle these issues, we propose coMpetition sOftening and coNgestion mItigation (MONI), a communication-efficient incentive mechanism for service pricing. Specifically, MONI employs a dynamic multiteam Bertrand game model to capture boundedly rational interactions among edge servers. It leverages capacity constraints to alleviate price competition and mitigate network congestion, while preserving the uniform stability of the game. Furthermore, MONI incorporates a genetic algorithm augmented with a truncated Gaussian distribution to minimize the disconnection of roaming devices. Experiments on synthetic and real-world industrial datasets demonstrate that MONI reduces recruitment costs and network congestion, increases the number of devices by 18.37%, and boosts model performance by up to 6.39% compared to state-of-the-art benchmarks.

Devices and servers in Federated Edge Learning (FEL) are self-interested and resource-constrained, making it critical to design incentives to improve model performance. However, dynamic network conditions raise energy consumption, while data heterogeneity undermines device cooperation. Current research overlooks the interplay between system efficiency and device clustering, resulting in suboptimal updates. To address these challenges, we develop BENCH, a bilateral pricing mechanism consisting of three core rules aimed at incentivizing participation from both devices and servers. Specifically, we first design a reward allocation rule, based on the Rubinstein bargaining model, which dynamically allocates rewards. Theoretically, we derive a closed-form solution for this rule, demonstrating BENCH achieves Nash equilibrium. Secondly, we design a device partitioning rule that leverages modularity to group similar devices, facilitating personalized edge aggregation to accelerate local data adaptation. Thirdly, we design an edge matching rule that employs the Kuhn-Munkres algorithm to balance the load at edge servers, thus minimizing the congestion. Together, these three rules enable hierarchical optimization of pricing and associations, effectively mitigating the impact of dynamic costs and device heterogeneity. Extensive experiments demonstrate BENCH's effectiveness in increasing device participation by 28.81% and improving model performance by 2.66% compared to state-of-the-art baselines.

Although vertical federated learning (VFL) has become a new paradigm of distributed machine learning for emerging multiparty joint modeling applications, how to effectively incentivize self-conscious clients to actively and reliably contribute to collaborative learning in VFL has become a critical issue. Existing efforts are inadequate to address this issue since the training sample size needs to be unified before model training in VFL. To this end, selfish clients should unconditionally and honestly declare their private information, such as model training costs and benefits. However, such an assumption is unrealistic. In this article, we develop the first Truthful incEntive mechAnism for VFL,$\mathbb {TEA}$, to handle both information self-disclosure and social utility maximization. Specifically, we design a transfer payment rule via internalizing externalities, which bundles the clients’ utilities with the social utility, making truthful reporting by clients be a Nash equilibrium. Theoretically, we prove that$\mathbb {TEA}$can achieve truthfulness and social utility maximization, as well as budget balance (BB) or individual rationality (IR). On this basis, we further design a sample size decision rule via linear programming (LP) relaxation to meet the requirements of different scenarios. Finally, extensive experiments on synthetic and real-world datasets validate the theoretical properties of$\mathbb {TEA}$and demonstrate its superiority compared with the state-of-the-art.