With the advancement of the "dual-carbon" strategic goals, the ownership of new energy vehicles represented by electric vehicles (EVs) has shown rapid growth. In this context, electric vehicle aggregators (EVAs) have emerged as crucial intermediaries for large-scale EV-grid integration. Proposes a novel transaction decision-making mechanism for EVAs participating in electricity market, addressing the complex interactions among multiple stakeholders. First, EVs are categorized into V2G-capable bidirectional and charging-only unidirectional types based on their interaction modes. The operational boundaries of EVs are precisely characterized considering grid-connection states, thereby establishing the feasible region for EVA"s regulation capacity. Second, considering the interest conflicts among multiple EVAs and between EVAs and the Independent System Operator (ISO), a transaction decision model for day-ahead and real-time electricity market is developed based on Nash-Stackelberg game theory. The bi-level optimization problem is then transformed into a single-level formulation through KKT conditions and strong duality theory. Case studies demonstrate that the proposed approach can provide an effective reference for EVAs participating in electricity market transactions, significantly enhancing the utilization of adjustable EV resources while improving economic benefits.