Re: Moral Hazard with Auctions

Interesting experience you had there, but I think that there a a number of reasons why it didn't play out the way you think it did. Also, what I find interesting is that again we found out that people are irrational, rather than rational. Here is a very quick rundown of how I see your problem.
First, you assumed irrationality from your bidders. You posted the ad as a first price sealed bid. That should have resulted in bids that are close to people's valuations. You assumed it did not (hence you assumed irrationality) and decided to turn it into a second price sealed bid auction, which resulted in an increase in your profits.
Second, you introduced signals into the equation. By offering the two top bidders the chance to increase their bids, you allowed them to get signals, which turned the auction from a sealed one into an open one (rather close to an English style auction). This also changed the dynamics and should have allowed you to extract as much surplus as possible, but still end up with a second best solution. However, you introduced another constraint by limiting the number of bids you would accept from your top two bidders. This cut into your surplus, because now you gave them information that allowed them to determine that your reservation price has long been met, and also that you follow a less than rational path in your decision making.
All in all, I think you reduced your potential profit by showing eagerness to conclude the deal. Additionally, you reduced your profit by engaging in an auction style that resembled more an open auction rather than a closed one. Open auctions never yield the best outcome. I think, if we return to the assumption of rationality (which was clearly violated by your bidders) that you can achieve the first best solution from your perspective with a model that follows something like this:
--announce the auction
--contact your top two bidders, let them know what the highest bid right now is and ask them to turn in a single bid, sealed and the winner of the bid takes the tickets
--get the bids and give the tickets to the highest bidder.
This way you circumvent the problem of irrationality in the first bid to a certain extent. While people may be irrational in their first bid, by limiting the bidding war to a single second step you maintain the bid as a closed one, and thus you can extract their valuation. Continuing to accept small incremental changes (or even large) would result in a second best solution.
However, removing the rationality constraint and allowing for incomplete information inclusive of one's own valuation, your solution may be more appropriate. I think this may be an interesting research case in which we allow signals/changes in information sets to affect our valuation, thus the result of an English auction may yield more surplus to the seller than a sealed auction.