Minimum bid rule for Monopoly auctions
We have played with a minimum 1st bid of 1/4 the price of the property (to vary with property value, but to allow for unchallenged bids to be profitable from immediately mortgaging; this puts upward pressure on the 2nd bid, pushing it towards the mortgage price). Incremental bids are then at least the no-house rent amount (and so also varies with property value).