The evolving landscape of edge computing envisions platforms operating as dynamic intermediaries between application providers and edge servers (ESs), where task offloading is coupled with payments for computational services. Ensuring efficient resource utilization and meeting stringent Quality of Service (QoS) requirements necessitates incentivizing ESs while optimizing the platforms operational objectives. This paper investigates a multi-agent system where both the platform and ESs are self-interested entities, addressing the joint optimization of revenue maximization, resource allocation, and task offloading. We propose a novel Stackelberg game-based framework to model interactions between stakeholders and solve the optimization problem using a Bayesian Optimization-based centralized algorithm. Recognizing practical challenges in information collection due to privacy concerns, we further design a decentralized solution leveraging neural network optimization and a privacy-preserving information exchange protocol. Extensive numerical evaluations demonstrate the effectiveness of the proposed mechanisms in achieving superior performance compared to existing baselines.
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