The travellers' dilemma

[wazzickle]

Inspired by the discussion on cutting off our noses to spite our faces in the negotiating position with the eu.

Two travellers are returning from a distant destination, carrying back identical, valuable artefacts. However, their transit crashes, and their artefacts destroyed. The airline operator tells them he will compensate them, and that they should name their price, between $2 and $100, but need to do so without communication between each other or any form of planning ahead.

If they both name the same amount, that is taken to be true amount, and they will each be paid that amount. If one names lower than the other, however, that amount will be taken to be the correct amount. That traveller will receive an 'honesty bonus' of $2 more than that price; the other traveller is taken to be a liar, though, and will receive $1 less than that amount.

What amount of money should you claim is the price of the artefact?

1) $100
2) $99
3) $50
4) $3
5) $2
6) else

And why?

[jimbouk]

Two travellers are returning from a distant destination, carrying back identical, valuable artefacts.

How much are they actually worth? Being an honest man, I'd name that price...

[virtuo]

Did the travellers know each other? Did they buy the artefacts, as in do they have a known value?

My instinct would be to claim the maximum amount, as it's guaranteed as long as the other guy also claims it. But I'd need to be sure the other guy isn't an idiot.

[wazzickle]

Sorry, I forgot to specify, they are both entirely rational and know the other to be entirely rational. They were not bought, it is not known exactly how much they're worth, for the sakes of this problem you could assume that the artefacts are probably worth more than $100, but that this problem is how the airline insurance works out how much to pay out.

[TheAnimus]

So logically it would be $99, as that would provide the maximum return ie $101 if the other person is 'honest', and $99 if the other person is 'dishonest'. Complete no brainer.

[wazzickle]

So logically it would be $99, as that would provide the maximum return ie $101 if the other person is 'honest', and $99 if the other person is 'dishonest'. Complete no brainer.

If you said $99 and the other guy says $100, you would indeed get back $101, but if he chose lower than $99, you don't get $99, you get $2 less than what he said.

If the aim of the game were 'maximizing potential returns', you might be right. But if you're both entirely rational, the other person will be aware that you will be going for this strategy, and could either neutralize your strategy by going for $99 himself, or increase his own potential returns by underbidding you with $98. So if the aim of the game is 'maximizing returns', it's not quite a no brainer.

[Smudger]

It seems if the value of the artefact is more than the offered payment, you would go for the maximum offer, and hope the other guy agreed...

[Ttaskmaster]

but that this problem is how the airline insurance works out how much to pay out.

Oh, well that makes it easy then...

$100 value, minus $35 Admin fee, $25 Processing charge, $35 independent valuation costs, $10 fee to courier out the payment cheque, plus $75 legal advisor charges.

So regardless of any value in the artefact, the travellers *each* owe the insurance company $180.

[wazzickle]

It seems if the value of the artifact is more than the offered payment, you would go for the maximum offer, and hope the other guy agreed...

Implicit within the idea that both parties are entirely rational is that, as you've got the same information, you will be able to predict the others' strategy, thus you can maximise your returns by asking for $99 if you know he's going to say $100.

[Smudger]

Implicit within the idea that both parties are entirely rational is that, as you've got the same information, you will be able to predict the others' strategy, thus you can maximise your returns by asking for $99 if you know he's going to say $100.

For $1 extra, I wouldn't care...

[TheAnimus]

If you said $99 and the other guy says $100, you would indeed get back $101, but if he chose lower than $99, you don't get $99, you get $2 less than what he said.

If the aim of the game were 'maximizing potential returns', you might be right. But if you're both entirely rational, the other person will be aware that you will be going for this strategy, and could either neutralize your strategy by going for $99 himself, or increase his own potential returns by underbidding you with $98. So if the aim of the game is 'maximizing returns', it's not quite a no brainer.

Why if both actors choose $99, do any one get punished? The point is they don't get the reward unless I'm having one of my dyslexic retard moments and totally miss reading the rules.

No one would choose $98, as that would only be the same return as the $100, there is no benefit unless you wish to hurt the other actor.

The question is, would it be $100 or $99 (getting $101 potentially, assuming a rational actor). Now then it's classic prisoner's dilemma of co-operate or betray, we know everyone chooses betray, so you choose $99.

[TeePee]

No airline is giving you anything without a receipt. Your best bet is your travel insurance provider.

[Smudger]

If you both name the same price, you get that

[Ttaskmaster]

Two travellers are returning from a distant destination, carrying back identical, valuable artefacts. However, their transit crashes, and their artefacts destroyed.

Also, you might want to rephrase ^this part a little... I had been imagining two ethnic itinerant fellas in a large white beat-up old Ford van, expecting some kind of Daily Mail rant to follow!!

[big_hairy_rob]

Why is an airline operator compensating them for valuables destroyed in a transit crash? Clearly they haven't flown, so the insurance claim would be fraud...

Assuming that it's not then $100 should generate the highest price for both people ($200), while anything lower (say $100 and $99) would generate a maximum return of $101 + $98 or $199, so the maximum return happens should they both request the maximum amount, otherwise the price per person would be lower.

This assumes that there are actually two people and they can actually claim.

[wazzickle]

Amusing distractions aside, I'm not sure I explained it properly - you're all (presumably) a bright bunch.

In any case. Game theory suggests the answer is $2 - assuming you start with $100, as the other traveller is entirely rational, he will be looking to maximise his own return and select $99. Knowing that will be his strategy, you underbid him with $98, and he changes with $97, all the way until $2.

This is a fairly useful analogy to a bunch of conflicts, including, most obviously, nuclear deterrence.

The 'real' answer is clearly some mix of $99 and $100. This leaves you with a range of payouts between $99 and $101. The key here is that bidding $2 does not maximize returns, but, rather, minimizes them, through the logic simply of trying to beat the other guy. What the ratios would be is a question for smarter men than me, but it could be as simple as half and half. But game theorists actually insist that the only, correct answer, is $2. Which is pretty stupid imo.