Mobile Edge Computing (MEC) deploys edge servers close to end-users to address their computing requirements, with an emphasis on minimizing latency and enhancing security. However, the significant deployment costs associated with edge servers and the potential for resource wastage due to redundant deployment by various Edge Infrastructure Providers (EIPs) highlight the importance of adopting edge federation architecture. This architectural approach aims to deliver superior computing services tailored for MEC scenarios. Nevertheless, effective resource allocation and pricing strategies are crucial to ensure optimal resource sharing within the edge federation. This paper presents a game-theoretic model involving three primary stakeholders: terminal users, resource demanders within the federation, and resource providers within the federation. The game among these stakeholders is structured into two levels, with negotiation rounds playing a pivotal role. At the first level, the game outlines the initial resource demands of terminal users and the initial pricing by EIPs, while also considering the influence of historical pricing trends on resource demands. The second level focuses on defining the psychological expectations of resource demanders within the federation and the initial pricing by resource providers. To solve this game model, this paper introduces the Tripartite Game Pricing Approach (TGPA). Simulation results corroborate that TGPA outperforms existing pricing approaches, yielding higher total revenue for the edge federation and ensuring a certain utilization of computational resources within acceptable time constraints.