The Ultimatum Game (here) is as follows:
There are two players, and an amount of money they can divide. The first player proposes how to divide the sum between the two players, and the second player can either accept or reject this proposal. If the second player rejects, neither player receives anything. If the second player accepts, the money is split according to the proposal. The game is played only once so that reciprocation is not an issue.
Let’s say the amount if $100. If player-1 offers player-2 a payout of $99 for player-1 and $1 for player-2, is it irrational for player-2 to reject the offer?
The reasoning ‘yes’ usually goes as follows: if player-2 accepts, he gets $1. If he rejects, he gets $0. $1 > $0. Therefore, it is rational for him to take the $1.
The obvious problem is: the payout includes emotions, which are not included in the explicit analysis of the payouts of the game above. Rejecting an offer such as 1% of the total sum in the case above may lead to a feeling of retribution, for example. A feeling of retribution is a good. This is not included in the calculus of the payouts above.
Rationality comes from ratio, which involves comparing two things. In this case, the relevant ratio is “utility if accept” : “utility if don’t accept”. Emotion can impede an accurate assessment of the ratio, but here the feeling of retribution is part of the value on one side of the ratio. It is no longer $1 : $0, but $1 + emotional payout : $0 + emotional payout. It is easy to imagine how the right side of the ratio might become a lot bigger than the left side.
The bigger question I have, then, is: is a player being irrational if he accepts the offer? Based on the various payouts not included in the explicit description, my guess is yes, he is being irrational in accepting the specific kind of offer above. Not only is it not irrational to reject the $1, but he will be much better off rejecting the offer.
The above is about emotions in the payout, but what about being emotional while assessing the payout? Although being emotional when assessing payouts can interfere with one’s assessment, emotion can also inform one’s assessment, as emotion is basically a mechanism we have to synthesize (large amounts of) information, that would be intractable for the ‘rational’ part of the brain to work through, or that we have gained (presumably) through an evolutionary process. A feeling of retribution is telling us important information, in this case about what is the appropriate response to such a proposed sharing of resources in a more natural situation. Although in this situation the feeling of anger at such an offer may be outmoded, regardless the feeling of retribution one gains from spurning the offer is still a good in itself.
Why do we have a feeling of retribution, or other emotional aspects of a payout either way? Humans are social animals, so fair sharing is an important part of surviving. Emotions related to that are an important part of survival. We can’t turn the emotions on or off at will. Therefore, they need be included in an analysis of the payouts from games like these. Why is money important? Because it brings goods that are usually emotional, such as feeling good when drinking a coffee, or feeling good because one has higher financial status, and so on.
Reclaiming rationality means thinking more about emotion in payouts and assessment.
Thanks to Sacha for bringing the Ultimatum Game to my attention.