Ultimatum Game Results

Today I was planning on looking at the 'solution' to the ultimatum game and how it relates to what happens in the pirate puzzle if the last pirate breaks form. Unfortunately I'm not a good enough/fast enough writer to find a way to pull those two things together and this post was just looking like a big wall of unrelated text. So I'm going to split things into two and delay talking about crazy pirates for another day.

Yesterday I mentioned the Ultimatum Game where Alice is asked to divide $100 between herself and Bob. Bob then votes on the split and either the split carries or you both get nothing. If we all behaved like the puzzle pirates from two days ago then the correct split would be 99-1 and the stranger might be sad but would surely accept. One dollar is better than no dollars, after all.

It turns out in reality people aren't perfectly logical beings. I haven't been able to find actual data from most of the experiments which were run, only summaries from people who may or may not know what they're talking about. But it seems like in general Alice seems to offer much closer to a fair split, and with good reason. Bob frequently rejects splits which he views as being unfair. Apparently when you get into the $80-$20 split range more than 70% of splits are rejected.

I was talking about this with Andrew yesterday and he said that it's an interesting thought experiment while not much is on the line but if you were splitting up, say, $100k then all of a sudden the $20k seems like it should get taken more often, right? It turns out researchers thought of this too and ran the experiments with huge sums of money. To do so they went to a less developed country and started offering large sums of local currency. I found one study that took place in north-eastern India. The average yearly income in those villages was reported to be around 17k rupees and they were offering 20k in their highest stakes experiment. So they were giving these people more than a yearly salary in one game! They mucked with the experiment a little by straight up telling their Alice's that the optimal strategy is to offer as little as possible to Bob while having Bob still say yes. (They did this because they were trying to test how Bob played the game, not how Alice played the game, and all previous experiments were plagued with too many high offers. It turns out people just play nice too often!)

They succeeded in lowering the average offer significantly with those instructions. They also succeeded in showing that once you start offering a huge amount of money the behaviour changes.  When they were splitting up 200 rupees a full 50% of Bob's said no to offers under 10% of the pot. When splitting 20000 rupees only 5% did. It's hard to say no to a month's worth of money even when you know someone is 'screwing' you by taking 12 months himself. (Also of interest as the stakes got higher Alice would take a bigger chunk for herself. I guess the thinking is that if Bob is pretty much guaranteed to take a month's salary there's no point in giving him even more than that, right?)

A very interesting result came from an experiment done in New Guinea. Apparently the culture there is based on reciprocity. (As Sheldon would say, "You haven't given me a gift, you've given me an obligation!") There Alice would sometimes offer Bob more than half of the money. And Bob would say no!

So it turns out game theory doesn't really apply to a lot of these situations. There's something more at work than just maximizing incoming money. The concept of fairness was brought up a lot in the articles I was reading. Or maybe it's not a stranger and you realize you actually have to live with them going forward so you're better off giving them a 'fairer' shake so they're not bitter at you forever. It seems like the psychoeconomists are looking into it still. I find it interesting, anyway.