Federated Learning (FL) is an innovative learning paradigm that allows multiple devices to collaboratively train a shared model without uploading the raw data to the cloud, thereby enhancing privacy and security. Leveraging Mobile Edge Computing (MEC), Hierarchical Federated Learning (HFL) can further reduce the communication overhead, thereby increasing the efficiency and scalability of FL systems by enabling model aggregation at the network edge. However, this framework often encounters security challenges, such as single points of failure and the risk of malicious model tampering. To address these challenges, researches have employed blockchain technology to enhance the security of FL systems, but most of these solutions incur significant resource burdens due to the intensive computation demands of blockchain consensus mechanisms, such as Proof-of-Work (PoW). In this work, we aim to explore a lightweight blockchain-enabled federated learning (LBFL) framework that utilizes the Delegated Proof-of-Stake (DPoS) consensus mechanism, which employs a simple voting process to elect a small number of candidate block producers (known as delegates) to aggregate the FL model and produce blocks. This framework significantly reduces the number of consensus nodes, thereby minimizing resource consumption during the consensus process. We study the joint optimization of mobile device association, bandwidth allocation, computing frequency management, and block producer selection, aiming to minimize the overall delay and energy consumption. To address the challenges posed by discrete and continuous decision variables, we decompose the problem into three sequential subproblems and solve them iteratively. Simulation results show that compared with the existing benchmarks, the proposed scheme can reduce overall delay and energy consumption by 15% to 22%.

Blockchain is a decentralized and secure digital ledger system that ensures data integrity through immutable records and cryptographic consensus mechanisms. However, in mobile blockchain networks, the computation-intensive proof-of-work (PoW) mining process often imposes a significant burden on mobile users (MUs) who serve as miners, particularly given their limited computing resources. Mobile edge computing (MEC) offers a promising solution to alleviate the burden on MUs, by enabling them to offload their mining tasks to nearby edge servers. While existing studies have explored MEC-assisted blockchain networks in both single-server and multi-server scenarios, they often overlook crucial aspects of blockchain networks, such as the transmission and computation delays inherent in the mining process. In this work, we investigate a more realistic MEC-assisted mobile blockchain network, where mining tasks are explicitly modeled with delay constraints to better capture real-world performance challenges. To analyze the strategic interactions between MUs and edge computing service providers (ECPs), we formulate a two-stage multi-leader and multi-follower Stackelberg game, which consists of an ECP Resource Pricing (ERP) game at Stage I, and an MU Resource Competition (MRC) game at Stage II. Specifically, in the ERP game at Stage I, ECPs, acting as leaders, set the resource prices for MUs; and in the MRC game at Stage II, MUs, acting as followers, determine their computing resource demands based on the prices of ECPs. We first prove the existence of Nash equilibrium (NE) for both games, and then derive the closed-form conditions for the NE of the MRC game at Stage II. Based on the above, we further propose a sub-gradient-based resource pricing algorithm that can converge to the NE of the ERP game at Stage I. Simulation results show that, when compared to the centralized cooperative solution, our proposed non-cooperative game approach can significantly reduce the computational complexity, while incurring only a modest performance degradation, e.g., the social welfare loss ranges from 6.64% to 9.96%.

Mobile edge computing (MEC) is a promising technology that enhances the efficiency of mobile blockchain networks, by enabling miners, often acted by mobile users (MUs) with limited computing resources, to offload resource-intensive mining tasks to nearby edge computing servers. Collaborative block mining can further boost mining efficiency by allowing multiple miners to form coalitions, pooling their computing resources and transaction data together to mine new blocks collaboratively. Therefore, an MEC-assisted collaborative blockchain network can leverage the strengths of both technologies, offering improved efficiency, security, and scalability for blockchain systems. While existing research in this area has mainly focused on the singlecoalition collaboration mode, where each miner can only join one coalition, this work explores a more comprehensive multicoalition collaboration mode, which allows each miner to join multiple coalitions. To analyze the behavior of miners and the edge computing service provider (ECP) in this scenario, we propose a novel two-stage Stackelberg game. In Stage I, the ECP, as the leader, determines the prices of computing resources for all MUs. In Stage II, each MU decides the coalitions to join, resulting in an overlapping coalition formation (OCF) game; Subsequently, each coalition decides how many edge computing resources to purchase from the ECP, leading to an edge resource competition (ERC) game. We derive the closed-form Nash equilibrium for the ERC game, based on which we further propose an OCFbased alternating algorithm to achieve a stable coalition structure for the OCF game and develop a near-optimal pricing strategy for the ECP's resource pricing problem. Simulation results show that the proposed multi-coalition collaboration mode can improve the system efficiency by 12.64% ∼ 17.63%, compared to the traditional single-coalition collaboration mode.

The mining process in blockchain networks generates substantial computing consumption, which can be very challenging for miners operated by mobile users (MUs) with limited computing resources. Cloud mining service (CMS) offers a viable solution to this challenge by allowing miners to offload computation-intensive mining tasks to cloud mining providers (CMP) with abundant resources. One key problem in such a scenario is to design an effective resource pricing mechanism for the CMP. Existing researches in this field mainly focused on the differentiated pricing mechanisms, where different MUs are required to pay different prices, which are often very complicated. In this work, we explore an efficient resource pricing mechanism, where the CMP sets a uniform price for all MUs but regulates the quality of resources for different MUs. Such a mechanism can capture the key essence of differentiated pricing and greatly reduce complexity. Based on this novel mechanism, we establish a two-stage Stackelberg game between the CMP and MUs, which consists of a resource pricing and quality control problem (for the CMP) as the first stage and a mining competition game (among all MUs) as the second stage. We derive the closed-form Nash equilibrium for the mining competition game in the second stage and propose a successive convex approximation (SCA)-based algorithm that converges to the near-optimal solution in the first stage. Simulation results show that the proposed iterative algorithm can improve system utility by 32.5% compared to other schemes.

Mobile edge computing (MEC) is a promising technology for improving the efficiency and security of mobile blockchain networks, by allowing miners with limited computing resources to offload the computation-intensive mining tasks to edge computing servers that are proximate to them. Collaborative block mining can further improve the mining efficiency and increase the miner profit, by enabling multiple miners to pool their computation resources and transaction data together to mine new blocks collaboratively. Thus, an MEC-assisted collaborative blockchain network can leverage the advantages of both technologies, offering superior efficiency, security, and scalability for blockchains. While existing research in this area mainly focused on the single-coalition collaboration mode where each miner can only join one collaborative coalition, this work explores a more comprehensive multi-coalition collaboration mode, which allows each miner to join multiple collaborative coalitions. To analyze the miner behavior in such a scenario, we formulate a novel two-layer sequential game, consisting of a coalition formation game as the first-layer and an edge resource competition game (among the formed coalitions) as the second layer. Specifically, in the first layer, each miner acts as a game player and selects multiple coalitions to join, leading to an overlapping coalition formation (OCF) game among miners. In the second layer, each established coalition acts as a game player and decides the amount of edge computing resource to invest, leading to an edge resource competition (ERC) game among coalitions. We derive the closed-form Nash equilibrium for the ERC game, and propose an iterative algorithm that converges to a stable coalition structure for the OCF game. Simulation results show that the proposed multi-coalition collaboration mode can improve the system efficiency by 34.1% ~ 54.3%, compared to the single-coalition collaboration mode.