In the emerging cloud-edge-end computing networks, edge servers possess more constrained resources and face greater task offloading pressure than centralized cloud servers due to the surge in mobile applications and data. Concurrently, the presence of multiple edge service providers introduces additional challenges, including competition among servers, disordered resource pricing, and a lack of coordination in edge and cloud resource allocation. To address these issues, we propose a novel approach aimed at optimizing task deployment, resource pricing, and system coordination. First, we develop a competitiveness model to facilitate efficient edge-side task allocation while addressing the challenges of resource pricing under competitive conditions. Second, we design a transformer-based task prediction model to enhance the accuracy of resource demand forecasting, thereby enabling more effective edge-cloud resource allocation. To achieve these objectives, the system's interaction is structured into two distinct stages. This division simplifies the problem-solving process and ensures that the long-term goal of maximizing benefits for all stakeholders—edge service providers, cloud providers, and end-users—is achieved. The proposed solution not only improves task offloading efficiency and resource utilization, but also promotes fair competition and pricing transparency across the system.