In other words, a bidding war is a situation where two or more buyers are interested in an item (such as a house or a business) that they make increasingly higher-priced offers in attempts to outbid others and win the ownership of the item.
[1] In real estate, a potential buyer can increase their bid in a number of different ways.
Some common ways a bidder can increase their bid such as offering a higher purchase price, reduce the number of contingencies, pay with cash or even write a letter to appeal to the seller.
These are all strategies that are proven to increase the odds of the buyer winning the bidding war.
The ask or offer price on the other hand is the lowest price a seller of a particular stock is willing to sell a share of that given stock.