Ultimatum Game - A Twist

OK, I’ve seen a couple of threads on the Ultimatum Game, and wanted to ask a follow-up question, but didn’t want to derail any of the existing threads.
If you haven’t read any of the other threads, in an Ultimatum Game there are two players. The first player is asked to split $1,000 between the two players. The second player then accepts or refuses the split. If the second player refuses the split, neither player gets anything. For example, if the first player offers the second player $100 and the second player accepts, then the first player gets $900 and the second player gets $100. If the second player refuses, then neither player gets anything.

In this variation of the game you are the second player. You are told that the first player is in the other room and you will communicate only through the observer. You will never meet the first player; you arrive separately, you will leave separately, and you will never know who the first player is.

The first player makes you an offer through the observer. Imagine that it is the largest amount that you will not accept. E.g., if you tell yourself that you will turn down any offer less than $500, imagine that the offer was for $499 and so you turn it down.

Suppose that, after you turn the offer down, the observer tells you that there never was a first player, and there never was $1,000; they simply offered you $499, along the description of the game, to see what you would do.
Do you still think that your decision was the best one? Does this change your approach to the version of the game in which there really is a first player who you just never meet?

Doesn’t change anything. It’s equivalent to an opponent in Poker telling you that they were bluffing, or that they really did have a strong hand. It didn’t affect your calculation then, and it doesn’t affect it now.

As I said in one of the other threads, I’d accept a single dollar, because free money is free money, and "some money is better than “no money”. So, it would make no difference to me whether or not there really was a “Player 1”.

In the strick form of the Ultimatum Game, there is no bluffing; in fact there’s no communication between the players. Player 1 writes down a number, which he cannot change, and player 2, in the other room, either accepts or refuses. No counteroffers, no bluffing, just the single decision.

Out of curiosity, what is the largest dollar amount that you wouldn’t accept?

I guess I don’t understand the game. Since I cannot negotiate with player 1, how is it to my advantage to refuse any offer, even 1 cent?

Unless you postulate that I will be playing again, with the same person, or with different people who will know the outcome of my first game, it makes no sense to refuse money.

Hmmm, interesting. So instead of screwing myself over to screw somebody else over, I just screwed myself over.

Economic theory says that the best thing to do is accept any amount offered. Actual practice suggests that people will turn down “unfair” offers, even though it costs them money, simply to punish the other player. This is true even though they never meet the other player, before or after the game.

I said I’d never refuse any money whatsoever because I never thought it was mine to begin with. I’d accept the minimum offer. So the arbiter would have to offer me $0 by the rules of the OP. So when he says there’s no player, that’s cool because there was never any money either. So I’d shrug and walk away.

A variant of this experiment was actually conducted. The researchers told the second participant (before they made their accept / reject decision) that the split had been randomly determined by a computer. On average, this resulted in the second participant accepting a considerably lower offer than when they thought the split was made by another human player.

Apparently people are more willing to accept a low payout resulting from “the luck of the draw” rather than from someone else’s perceived greed.

My decision was made with the best information I had available at the time. That’s the best anyone can do. Obviously in light of this new discovery I end up looking rather silly, but that’s neither here nor there, the die is already cast. It doesn’t impact the quality of the decision I made at the time.