Under the first-price rule each bidder submits a sealed bid stating the price that she will pay if she wins the auction. The bidder then opens all the sealed bids and ranks the bids in a descending order. The bidder who has submitted the highest bid wins the object and pays a price equal to her bid.
Tie-breaking rule: If the two highest (or more bids) are equal, then the tie is broken according to some pre-determined rule. For instance, the bid that has the earlier time stamp for submission may be awarded the item. The tie-breaking rule may even be random with one of the equal bids randomly chosen to be the winner.
An auction like this is viewed as a game and we borrow ideas from game theory to predict how bidders will bid and what the outcome of the auction will be.
I find it easier to understand the predicted bidding behavior and outcome in a complete information set-up first before moving on to understand the incomplete information environment.Â