Because Arjuna or Mahārāja Yudhiṣṭhira was not king at that time, the financial control was not in their hands, and these people, sons of Dhṛtarāṣṭra, they were on the government political power. The financial control was in their hands. So they were giving enough money for maintenance to Dronācārya and Bhīṣmadeva. So they felt obliged. Of course, they knew everything. But externally, they felt obligation: "Arjuna, I am getting money from Duryodhana. So in this point of danger, if I do not join him, it does not look well. I am getting financial maintenance."
Of course, Arjuna did not ask him. Arjuna was satisfied with Kṛṣṇa. That's all. Kṛṣṇa also divided Himself. Because it is family quarrel. So He said, "I cannot take part with anyone and even if I take part, side, of any of you, I shall not fight. Directly I shall not fight. I may be on your side or that side, but I'll not fight." Still, Arjuna was satisfied. So Kṛṣṇa, in order to satisfy Arjuna, that "I shall not fight, but I shall become your charioteer. I shall drive your chariot." So in this way the battle was arranged, and when Dhṛtarāṣṭra inquired, kim akurvata sañjaya (BG 1.1), "What did they do?" He said, "Sir, don't be disappointed. There was no compromise.