The offers poured in, but one guy (A) offered a much larger amount. Then finally another guy (B) offered to top it. I told him to hang on because I owed A the chance to top the previous bid. I called the original high bidder told him of the offer and gave him the chance to raise his bid and he offered 50 dollars more (Bid: 1). I called B back and told him that he had to top Bid: 1. At this point I had not told him the amount of Bid: 1 and thought briefly about telling him it was much higher, a moral hazard problem we try to avoid in second price sealed bid auctions. Instead, I told him the true price and this was my reasoning:
If I tell this guy too high a price, he'll back out and my outside option will be Bid:1. I don't know what amount this is that will cause him to back out, but if I tell him the real amount he will top it or back out leaving me Bid: 1. Therefore my expected profit will be higher to be truthful. My incentive is to be truthful unless I know what his price elasticity looks like.
Exp. Profit = p(Bid: 1) + (1-p)(Bid: 1 +a), p is between 0 and 1, a is a high number
But if I'm truthful:
Exp. Profit = p1(Bid: 1) + (1-p1)(Bid: 1+e), where e=a small number, p1
I believe the uncertainty would push p close to 1 and certainty will push p1 close to zero. Therefore a would have to be very large for lying to be profitable. But I think this will almost never happen because a is bounded above by the bidder's internal valuation and we have almost no information about where that bound might be. Getting e more than the bid is preferable to taking the chance as a risk averse individual.
Now, what would prevent me from playing the two bidders off against each other? Well people generally don't like that and I run the risk of losing both of them if I do that. People want to like the person they buy stuff from and they could both back out if they think I'm running a game on them. I can get away with it once perhaps, but to continuously do it is much more difficult.
What do you think? Is there a self enforcing mechanism in this type of auction?
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