I’m spiteful? How about that other jerk? He made me do it.
But I could have just bid 3 cents. Then he should sit on his hands, right?
It’s not a crime he bid. Neither is it a crime to bid 99 cents plus his bid. But my question to you was, why bid at all?
I guess I’m just seeing it as a slippery slope. I think everyone agrees that nobody benefits from a pattern of escalating bids. The issue is when does that pattern begin?
Is it when the second player bids two cents to the first player’s initial bid? When the first player bids three cents knowing that the second player has committed money to the auction?
Thinking about it, I think the pattern originated at the very beginning. It started when the first player made an initial bid of one cent. He created an opening for the bidding war to begin.
It seems self-evident to me that a bidding war begins with the second bid. No one is in conflict with anyone else until the counterbid. “Creating an opening for the bidding war to begin” to me is like saying the guy who gets punched in the nose started the fight by walking out his door.
The opening is real. If the second player bids two cents and his opponent doesn’t counterbid, then he makes a profit of ninety-eight cents.
You can, of course, point out that the first player will counterbid - it’s irrational for the second player to assume the first player won’t bid three cents.
But if that’s the case, then it’s equally irrational for the first player to make a one cent bid and assume the second player won’t bid two cents.
It’s equally irrational for either player to make a bid that relies on the assumption that the other player won’t counterbid.
The only time when a player can rationally assume the other player won’t make a counterbid is when there is no opening for making a larger profit. That’s the reason why the ninety-nine cent bid is rational.
Whoever is lucky enough to get the first bid in is the equivalent of someone who finds 99 cents in the gutter, if only everyone were as rational as me. 
I assume the second player won’t bid because there is no good outcome that can occur if he does. There is no opening for profit the second a counterbid is made. That possibility is lost, except if someone simply concedes it and takes his own loss.
But the basis of that is essentially, “It’s okay for me to follow a strategy that could be foiled by an irrational counterbid because I can assume my opponent will not follow a strategy that could be foiled by an irrational counterbid.”
No, it’s much simpler: rational players will not make irrational counterbids. Period.
It’s a given we’re assuming rational players, right? Because in the real world, the answer is easy: never bid. Not first, not ever. This is supported by the well-established scientific fact, “The world is festooned with nitwits, so you can pretty much count on somebody doing something stupid.”
Exposing yourself to greater risk for no possibility of gain, to punish someone for not collaborating with you (despite the rules forbidding it) and to shape their future behaviour (despite the rules making this irrelevant) is also an irrational counterbid.
I got it. You think I’m an evil guy. I didn’t miss that point. I will have snatched 98 cents from the hands of the other bidder. I may spend extra time in purgatory as a result. And the risk is minimal. It would only be in a situation where even the most addle-brained sees he would be taking an even greater loss. ::shrug:: If we’re both a bit poorer, there you go. And you didn’t answer my question. Should I just bid 3 cents instead, and then the other guy will sit on his hands, right? And if he doesn’t, he’s punishing me for not handing him the dough, right? This is a lot of money, it’s important.
But it has nothing to do with collaboration. If someone refuses to play tic-tac-toe for money (paying a vig), that’s not collusion. It’s an acknowledgment that it’s a no-win.
It has nothing to do with evil motives or future games or luck or collaboration. It comes down to this: if it’s irrational to bid two cents in the expectation that the other guy won’t counterbid, how is it rational to bid one cent in the expectation that the other guy won’t counterbid?
I don’t know how else to explain it, and it’s clear we disagree. The only way anyone wins this is if potential counterbidders concede it. Period. If we’re all rational, we know this. If you counter my bid, and you’re rational, you’d have to know that I’ll bid $1.01. Because you know if I do that, there’s no incentive for you to counterbid (in Logical World). Any other third bid doesn’t amount to a disincentive. It’s only a bad move for you to counterbid, because it can only cost you. It’s why nuclear powers don’t make a first strike against another nuclear power. It’s completely logical (I think).
Unlike nuclear launches, this is not that earth-shattering a topic. Feel free to bid as you like whenever it comes up.
Come to think of it, there is a fundamental difference between the first bid and every subsequent bid, since the rules of the game are different when there’s only one bid from what they are at every time thereafter. The rules must necessarily include a special-case “if” statement for that case, since they simply don’t work otherwise.
As stated, the rules are that the highest two bidders both pay. But if there’s only one bidder, then it’s not possible for the highest two bidders to pay. So what the rules really mean is “if there are two or more bidders, then the highest two pay, but if there’s only one bidder, then only that one bidder pays”.
I’d say the two highest bids still pay and the two highest bids were zero and one cent.
What do you think the word rational means? Cause I don’t think that you’re using it in the sense that game theorists are.
In the informal description, yes, but I don’t really see why that’s relevant. In the extensive form description (see page 2 of this previously linked article), there’s no need to specify anything like that.
If it doesn’t have exactly two players, it’s not the dollar auction. One player auctions are not particularly interesting, and three or more player auctions are difficult to describe to an audience that doesn’t have a pretty strong background in game theory, so let’s stick to the two-player case.