Multi-access edge computing (MEC) and network virtualization technologies are important enablers for fifth-generation (5G) networks to deliver diverse applications and services. Services are often provided as fully connected virtual network functions (VNF)s, through service function chaining (SFC). However, the problem of allocating SFC resources at the network edge still faces many challenges related to the way VNFs are placed, chained and scheduled. In this paper, to solve these problems, we

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... ropose a game theory-based approach with the objective to reduce service latency in the context of SFC at the network edge. The problem of allocating SFC resources can be divided into two subproblems. 1) The VNF placement and routing subproblem, and 2) the VNF scheduling subproblem. For the former subproblem, we formulate it as a mean field game (MFG) in which VNFs are modeled as entities contending over edge resources with the goal of reducing the resource consumption of MEC nodes and reducing latency for users. We propose a on a reinforcement learning-based technique, where the Ishikawa-Mann learning algorithm (IMLA) is used. For the later subproblem we formulate it as a matching game between the VFNs and an edge resources in order to find the execution order of the VNFs while reducing the latency. To efficiently solve it, we propose a modified version of the many-to-one deferred acceptance algorithm (DAA), called the enhanced multi-step deferred acceptance algorithm (eMSDA). To illustrate the performance of the proposed approaches, we perform extensive simulations. The obtained results show that the proposed approaches outperform the benchmarks other state-of-the-art methods.