Drupada acknowledged Yudhishthira's arguments but was still coming to grips with his daughter becoming polyandrous. Maharshi Vyasa then arrived at the scene, took Drupada aside, and told him the story of Draupadi's past life.
In her previous life, Draupadi was the daughter of a sage. She had prayed to Lord Shiva for a husband. When Shiva finally appeared, she eagerly repeated her wish five times. So Lord Shiva blessed her with five husbands. Drupada finally accepted Lord Shiva's boon, albeit hesitantly.
Maharshi Vyasa presided over Draupadi's marriage to all five Pandavas. Sage Dhaumya lit the sacred fire, chanted the mantras, and sat in the wedding-hall with the newlyweds.