Sunk Costs and Optimal Bidding Strategy for an Authentic $100 Bill Auction

[Jameson]

You are in an economics class where the topic of the day's lecture on "sunk costs" so to demonstrate your professor has a short auction. The item available is an authentic \$100 bill, worth \$100 current dollars of course. The bidding starts at \$1 and must increase by at least \$1 over the previous bid.

There is one extra rule though: If you are the highest bidder you win the money but if you are the second highest bidder you must pay your losing bid nevertheless.

You and a group of students begin the bidding and quickly it comes down to you and one other person. He bids \$98, you bid \$99 and he bids \$100.

What is the best strategy from this point on? Try to find a way to describe your optimal decision from this point on and assuming your opponent can make a large range of choices as well from this point on.

(Note: this POTW is a little different so to receive recognition for this problem your strategy must be non-dominated by another possible strategy and you must give your reasoning)
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[Jameson]

No one answered the problem in the way I intended, but since the goal of the situation (to win the most money or lose the least amount of money) might not be clear I will award MarkFL credit for this week's POTW.

1) MarkFL

Here is my solution:

Spoiler

You last bid \$99 so you stand to lose \$99. If you can lose less then this or make a profit from this point on then you are in a better situation. Your next minimum possible bid is \$101, which is a net of -\$1 if you win the auction, so this is clearly better than losing \$99.

In fact you can continue to increase the bid amount until \$199 and not lose money compared with your current situation. If you bid \$200 or more then you lose even more money, so the max bid you should make from here is \$199.