Comment by roughly
2 years ago
Back when I was getting my econ degree, we were taught about the Ultimatum game, which goes like this: You get two participants who don't know each other and will (ostensibly) never see each other again. You give one of them $100, and they make an offer of some portion of it to the other. If the other accepts, both parties keep their portion - so, if A offers B $20, and B accepts, A keeps $80 and B keeps $20, if B rejects, both parties get nothing. Standard economic theory suggests A can offer $1 and B will accept, because otherwise B gets nothing. Spoiler for those of you who haven't seen how standard economic theory plays out in real life, that's not how the game went - typically, offers below ~$30 or so got rejected, because B was a real feeling person who felt like they were getting screwed and opted to punish A for doing so. The exception to this - the people who would take the $1 offer - were people who had been taught economic theory. It turns out you _could_ screw them over and they'd pat themselves on the backs for being very wise.
The "tragedy of the commons" is another one of those parts of standard economic theory that never actually played out in reality - we've got examples from all over the world of communities implementing practices and often entire belief systems that led them to be responsible stewards of shared resources without requiring unilateral ownership of that resource and singular acquisition of the benefits of that stewardship, and yet first on the lips of every modern capitalist when describing why they're at a disadvantage if they're not the ones polluting the water supply is the tragedy of the commons.
This reminds me of Lord of the Flies. The real version of the events turned out very differently.
https://www.newsweek.com/real-lord-flies-true-story-boys-isl...
Rebecca Solnit wrote a book, "A Paradise Built in Hell", on how people behave during disasters, and found broadly the same thing - contra the prepper myths, most people most of the time faced with disaster come together to work cooperatively to help each other.
We're a fundamentally social species - we've got smaller brains than Neanderthals did, we're not a particularly tough species, but we're very, very good at cooperating with each other.
Each player can limit the other's income to $0 - the offerer can offer $0 and the receiver can reject any deal.
So then what's optimal? $50 seems obviously fair, but does that mean we ought to reject offers of $49 100% of the time? Not quite, to limit the opponent's expected income for an offer of $49 to $50 instead of the $51 they left for themselves, we can use a mixed strategy that only accepts the offer with probability 50/51. Extending that gives the opponent a benefit curve that is linear as they leave themselves more money up to $50 and then flat at $50 afterwards.
That's good, but we can make it better - if we accept offers for $X<$50 with probability 50/(100-X) - epsilon*(50-X), then their expected benefit curve is smooth and has a peak at $50, which is the most we can expect to make except against a generous opponent.
After all that, playing this game as stated against an unknown opponent there's a lot of uncertainty. Maybe all your opponents are entirely irrational and move at random. Maybe all your opponents have colluded and decided that $66 for the offerer and $34 for the receiver is fair and that's the only deal they'll make. But if you think that random actors in the universe are reasonably intelligent and can discover the equilibrium above with the thought worth putting into this Ultimatum game, the receiver strategy above properly aligns incentives.
> It turns out you _could_ screw them over and they'd
End up with a dollar in their pocket which they otherwise wouldn't have.
The Ultimatum game is a useful insight into human psychology: for one thing, it tells us who thinks that the defector in this equilibrium is better off than a counterfactual cooperator.
Ah, but they have their pride! Ok. My pride is not affected by someone else having 99 bucks they didn't earn, and myself $1 likewise. Maybe that other fellow really needed the money.
I don't know what the hell you're talking about. Your argument is incoherent. If you wanted to allocate the money according to the individual's utility of money, then a rule of thumb of $1 is going to be wrong. You should, given no information, assume that both have the same utility of money and that the utility of money is diminishing, favouring an even split.
Indeed. You’re very wise!
You may be interested in some of the foundational papers exploring game theory models similar to the Ultimatum game[1][2]. These are known as Iterated Prisoner's Dilemmas.
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[1] The Evolution of Cooperation (https://ee.stanford.edu/~hellman/Breakthrough/book/pdfs/axel...)
[2] Evolutionary Dynamics of Spatial Games (https://www.sciencedirect.com/science/article/abs/pii/016727...)
It's crazy how most political or economic systems would very obviously collapse in the real world almost instantly without some kind of voluntary moral contract (explicit or implied), yet we've got huge clumps of people demonizing one system or another based on the context of what happens when you implement it in a morally dead societal context.
Like there are a ton of people who smirk at your last paragraph and go "nuh uh, hashtag late stage capitalism"
A hundred percent. I've said this elsewhere, but a primary problem for at least American society at this point is we don't have a commonly-agreed upon moral system other than the market - things like Martin Shkreli buying drugs people need to live and jacking the price up are Bad, but we don't have a common language for describing why it's immoral, whereas our only real common shared language, the market, is basically fine with it as long as it's legal. A lot of the market logic works fine for society within constraints - optimize your costs, but not at the expense of your workers; increase your prices if you can, but don't be a ghoul about it; lobby for your position, but don't just buy a supreme court judge.
If you iterate the game, it’s obvious. I, as the responder, control the proposer’s income. Extend to infinity with knowledge of iteration and you reach symmetry between proposer and responder.
> If you iterate the game, it’s obvious.
We're shockingly bad at doing this in modern society. Our temporal planning horizon is somewhere between 6 months and 5 years, whereas our lifespans are around 75-80.
...in the real world, A tells B that he "sourced" the deal and therefore deserves a bigger cut and in the real world, B agrees up to a point (the $30 mark). Over time and rounds of playing the game, the A's of the world learn where the line is and optimize to stay on the correct side of it, only testing the other side 1-2% of the time to see if rules/behavior has changed.
Game theory only applies to sociopaths and economists, but I repeat myself.