The rapid development of smart devices has fostered the growth of Spatial Crowdsourcing (SC), where workers complete spatial tasks by traveling to specific locations. Task assignment is a key issue in SC due to the inherent complexity of matching workers with these spatial tasks efficiently. Previous studies on task assignment have primarily focused on optimizing worker-task matching within a single, centralized area, often ignoring scenarios that involve multiple independent service centers across an area. To address this gap, we introduce a collaborative multi-center task assignment problem, which focuses on scenarios where an SC platform manages multiple independent service centers within an area, shifting the focus from worker-level cooperation to exploring the solutions specific to multi-center coordination. We target the imbalances between available workers and unassigned tasks among different centers, aiming to maximize the total number of assigned tasks and minimize unfairness in inter-center collaboration. In particular, we propose an Iterative Multi-center Task Assignment and Optimization (IMTAO) framework. IMTAO operates in two phases: (1) center-independent task assignment based on an efficient sequential task assignment algorithm, and (2) inter-center workforce transfer based on a game-theoretic multi-center collaboration algorithm that ensures fair collaboration through bi-directional optimization. Extensive experiments demonstrate the efficiency and effectiveness of IMTAO in enhancing task assignment and improving collaboration fairness compared to baseline methods.