There is an auction for a house, with a List Price of $100K. There are only two bidders, who bid randomly, one after another. Their bids are in the $0 to $100K range. They don’t know what the other person bid (even if they did, it wouldn’t matter cause their bids are random). The way the auction works is as follows: the person who had the highest random bid wins the auction. However, the amount they pay is not of their bid, but the smaller bid from the other bidders. E.g. if A bids $35K and B bids $65K, B wins the bid and pays $35K for the house.
Question: What’s the expected value for the purchase price?