What’s wrong with the Traveler’s Dilemma

The Traveler’s Dilemma is a problem in game theory that goes like this (from Wikipedia):

An airline loses two suitcases belonging to two different travelers. Both suitcases happen to be identical and contain identical items. An airline manager tasked to settle the claims of both travelers explains that the airline is liable for a maximum of $100 per suitcase (he is unable to find out directly the price of the items), and in order to determine an honest appraised value of the antiques the manager separates both travelers so they can’t confer, and asks them to write down the amount of their value at no less than $2 and no larger than $100. He also tells them that if both write down the same number, he will treat that number as the true dollar value of both suitcases and reimburse both travelers that amount. However, if one writes down a smaller number than the other, this smaller number will be taken as the true dollar value, and both travelers will receive that amount along with a bonus/malus: $2 extra will be paid to the traveler who wrote down the lower value and a $2 deduction will be taken from the person who wrote down the higher amount. The challenge is: what strategy should both travelers follow to decide the value they should write down?

The first thought for many people is to say $100, or at least something very close to that.

A purely logical game theory approach results in both the players saying $2. This is because if you think the other player is going to say $100, then you are better off saying $99 as this will mean you get $101 and they get $97. If you realize this and you think that the other player will think the same and also say $99, then you should say $98. This line of thinking continues all the way down to saying $2, the minimum price.

In experiments players tend to choose $100 or very close to that. So what is going on?

Are people just irrational, or have they actually thought about it differently to a game theorist?

It seems to me that there is an argument that goes something like this:

If I choose $100 then, if the other player is totally rational and picks $2 then I get nothing and they get $4. If I had also been rational and picked $2 then I would have got $2. The difference is so small compared to the $100 that is on offer that it isn’t worth worrying about.

I might as well go for a high number and hope that the other player does so as well because the upside is so much bigger than the downside.

If I was going to play the game 50 times (with different other players so we can’t learn from each play of the game) then if I pick $100 each time I only need the other player to think the same one time in the 50 plays to do as well as just getting $2 each time. I don’t even need to co-ordinate with another player at $100, even if they pick $99 I will get $97, or if they pick $98, I will get $96. All way better than just getting $2. That they get a few dollars more than me if I pick $100 and they pick $98 really doesn’t bother me compared to ending up with just $2.

It seems pretty obvious to me why when this game is played in experiments that people choose high numbers and not the ‘rational’ choice of $2.

Today’s takeaway: Sometimes a bit of common sense will give you a better answer

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