To enhance the tactical planning capabilities of air defense systems, this paper develops a mathematical model for the coalition formation problem involving defense and control resources. Given the uncertainty in task scenarios and the high demand for rapid solutions, a multi-round auction algorithm, inspired by the British auction model in auction theory, is proposed. This algorithm is tailored for the formation of large-scale, heterogeneous, multi-agent coalitions. It improves task efficiency, optimizes the utilization of internal resources, and effectively addresses various potential threats. Through simulation experiments, a comparison with the integer linear programming method demonstrates that the proposed multi-round auction algorithm outperforms in key metrics such as total battlefield coverage, coalition stability, and other relevant indicators.