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Comment by troygoode | Hacker News Reader

This is incredibly silly because nobody will ever win a $20 for less than $20. As an example, let's say you & I are bidding on the $20 bill...

- After bidding for a while, I eventually place a bid of $19. At this point if you quit I make $1 and you lose $18.

- So now you bid $20. At this point if I quit you would break even and I would lose $19.

- So now I bid $21. Why bid $21 on a $20 bill? Because if I win I only lose $1 (rather than $19) and you lose $20.

- Now of course you would rather lose $2 than $20, so you're going to up the bid to $22, right?

I'd be interested in hearing from somebody more knowledgeable than I in game-theory: When should an agent quit bidding and accept their losses?

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I'm not an expert in game theory (I just had a half-completed econ degree once upon a time) but your analysis is spot on as far as I can tell. The pareto efficient outcome is for the first agent to bid $1 and for the second agent to quit without bidding. If there is a counter bid, then the first player will have an incentive to bid higher to avoid a loss. The second player would then have to counter bid in order to avoid a loss as well, and so on. At the $20 mark nothing changes: at that point both players are now trying to minimize loss. In any case, any other alternative from the pareto efficient $1 vs $0 bid will cause at least one agent to have a less preferable outcome, and hence that strategy would be chosen by a "logical" player.

Maybe more interesting would be to have each agent pick a bid in advance and reveal the bids simultaneously. Of course, the optimal strategy there would be to just bid as close to $20 as possible and hope for winnings to accumulate over time.

And in all of this it's not clear how the proprietor of this site will make money out of this deal.

Feel free to correct me if someone thinks this is wrong: perhaps there is a reason I never finished that degree. :)

So when does the bidding end?

There would be no reason to ever stop bidding. To avoid losing your money, all you have to do is make another bid. Your opponent will probably realize that if he doesn't out bid you again, he's going to lose a lot of money. So he out bids you. Which really pisses you off, until you realize that you can avoid losing your money again if you just make another bid. The game goes back and forth until one of you dies of an overdose. Then the game ends by default, but the winner will have a tough time collecting his money from his dead opponent.

The logical player wouldn't start bidding, unless they bid first. The illogical player presumably would stop bidding when they get tired (or have changed their billing information so that they can't get charged for their bids!).

Strange game. The only winning move is not to play.

A strange game :)

(http://www.imdb.com/title/tt0086567/quotes#qt0453844)

I stand corrected :)

How about a nice game of chess?

Users have a real shot at winning 20 dollar bills for less than face value. The reason for this is whenever a user cannot be paired up with another, he/she is paired up with a bot that chooses a max bid in advance and at random from a specified range. Once the auction hits this max bid, the system will quit and the user wins. The expectancy is in favor of the site, of course, but only marginally so.

How can a user trust your bot? So essentially, the only way to win at this game is for it to no longer be human-to-human interaction?

What exactly are you studying? Human willingness to gamble their money away based on the potential that the thing on the other end is really a stupid bot?

As you might imagine, I cannot control the results of user v. user auctions. But in an effort for users to trust my system's bot, I am prepared to post actual results of the last n real user v. bot auctions.

So, like a casino? Is that even legal?

Similar to a casino in that there is an element of chance that plays into the results. But dissimilar in that we're looking to build this into a fast-paced auction site for different items.

While I was getting my econ degree, all of my game theory classes and most of my classes that discussed game theory used this as an example.

There is no way to win if the cost of bidding is 0. If there is a cost of bidding and that cost is 10 cents for example, the only way to win is to bid $19.90.

However, if you're required to play, the most efficient outcome happens when you're the first to bid and you open by bidding $20. You're neutral on outcome and have satisfied your requirement to play the game.

I think there is a psychological problem with the game when the prize is so small and the incremental losses/bets are so small.

If the prize was say, $10,000 and the minimum bet increment was $5, people are more likely to bet higher and higher because losing $5 (at a minimum) is psychologically more defeating than losing $0.01 (at a minimum).

EDIT: Didn't realize the site was 1v1. It would work better if there were several people. There is absolutely no incentive for a player to bid beyond $20 if the losing player doesn't have to pay their bid.

When I read the loser will "forfeit" their bid I took that to mean the bid is voided or cancelled, so I don't lose anything. But in your scenario it is much harsher and therefore much much much more stupid of a proposition.

No, truly, in this style of auction (sometimes called an entrapment auction), the loser does genuinely have to fork over whatever their last (losing) bid was.

Which, in my opinion, is even worse than the bidding fee auction (used by swoopo) model.

Sites like this make me very angry.

My first instinct would be to see how the site handles large numbers. The best outcome would be for both (fake) participants to continuing bidding until the values wrapped and they both end up having to pay a large negative number, thereby winning big :)

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