Random Game Theory Question

[algorithmancy]

Here's the setup:

You and another contestant are given a prize pool of $1000, and the two of you have one minute to come to an agreement as to how to divide the money between yourselves. If you come to an agreement within the time limit, you each get your agreed-upon share, plus, you get an extra prize of $X and the other contestant gets an

Comments

[firstfrost]

Assuming I'm a person and not an algorithm, which may not be what you meant, my X=Y=0 strategy is probably something like "Argue for half, settle for a third, don't settle for less than a third unless their argument is crazily persuasive."

If X and Y are both lots bigger than $1000, settle for anything.

If X dwarfs both Y and $1000, offer them all of it.

If Y dwarfs both X and $1000, refuse to settle for less than half.

[algorithmancy]

You're definitely a person and not an algorithm, and you're expected to take the worth of a dollar into account.

If you prefer, you can also imagine the version where one player makes one proposal about how to cut the cake, and the other accepts it or rejects it on the spot.

So the size of the pot in the middle matters, presumably.
I notice that in the $1000 case, all your strategies are in terms of fractions of the pot. ("half of it," "all of it," etc.) Am I correct in assuming that as the pot gets life-changingly big, absolute dollar values start to matter more? For example, if there's a million dollars in the middle, and the other guy only offers you $50K of it, then it's still pretty expensive to say no, regardless of what X and Y are.

[firstfrost]

Well, in theory, but I've got a reasonably comfortable life at present, so my life doesn't need that much changing. It would be different if I was unemployed, my house was being foreclosed on, etc. Similarly, if the other guy was in the archtypical "kid has horrible disease, insurance has punted him, needs a million dollars" disasters, I'd be more willing to let him have it all. But if we were both people-like-me, I'd be willing to forgo $50K if the other guy was really being that much of a jerk.

(I suppose it would suck if there were hidden constraints that he had to offer only unfair deals...)

[algorithmancy]

Well, tell you what. I happen to be the sole proprietor of a top-tier Jerk Scolding business. Give me the $50K, and I'll make that guy feel like even more of a jerk than if you had said no. $50K buys a lot of jerk scolding.

[firstfrost]

I am apparently an altruist who holds grudges. :)

It isn't quite that I want him to feel like a jerk - I want him to feel like being a jerk was not a winning strategy. (Maybe this ties into it seeming like an iterated puzzle? I'm not sure.)

[algorithmancy]

Well, what if I frame it this way:

Your neighbor discovers oil on his property. If he builds a well in his back yard, he stands to make a million bucks. Due to an arcane law, you have veto power over the project. Your neighbor offers you $50K to not veto the project.

[tirinian]

While I understand what you're trying to do with that reframing, my immediate response is "hell no, $50K isn't nearly enough for me to live with an Oil Well next door." :-)

[firstfrost]

If it was minimal impact (which is what I'm assuming that reframing is for, because like tirinian, I'm not sure about living next door to an oil well, not to mention my housemate already clearly doesn't want to live next door to an oil well), then I don't veto the project, and I'm squeamish about taking the 50K for it.

But if it is oil on my property, I damn well do not give my neighbor $950K in order for him to not veto it and he is a jerk for suggesting it. :)

[arcanology]

And yet this is where game theory runs into the baked into human instinct of punishing members of the group who try to screw you over. I would bet until you get to people who basically need that $50K right now to avoid something horrible, most people will let their inner monkey out and prefer to punish the wrongdoer.

Game theory probably says you should take a buck, because that's a buck more than you had before. Game theory on the single game never makes any sense because humans always assume an iterated game where it's important to prevent people from screwing you again next time.