“Do banks purposely way underprice their foreclosures so they can get multiple offers and bid up the price?”
Answer:
Almost never.
If you see a foreclosure priced way below market, one or more people made a mistake. It may have been the agent, the “BPO” agent (who gave a second opinion on value), an appraiser, and/or someone at the bank.
But I can tell you after working with over 40 different banks selling their foreclosures, while they sometimes want to price their properties attractively, they definitely do not have a practice of drastically under-pricing them.