Game Theory 101: The Ultimatum Game

[@Historically-Innacurate]

On this day, a legend was born

[@VMLM3]

If I were Tommy, I'd get more satisfaction out of denying Angelica 11 cookies than from eating one. And I'd make sure Angelica knew that.

[@atomic7680]

Sure, but this is irrational behaviour. We assume rational agents in this game ;p

[@teamupleft7097]

Precommitment, if you can communicate that it's what you're doing, is a very powerful weapon. Of course, you can only reliably precommit if you know the rules of the game.

[@WavyCats]

@@atomic7680 It's entirely rational in real world applications. As the person above me stated, this is precommitment and it's very powerful. Also shows people that you can't be messed with, reducing the risk of later cheats.

[@alfredjovanovic2106]

Insidious consumption

[@jolly-rancher]

Economists get baffled when you behave that way I know because that's what I did in some of their experiments

[@GoatNews]

RIP to my good friend John Nash. I'll remember our conversations on the Dinky, playing chess at Princeton and hanging out at the Burger King on Nassau St. There's a lot that was never said about who you truly are. It will not be in vain.

[@ShaneH]

There is an incentive for Tommy to reject the one cookie: to punish Angelica for being stingy/unfair. The ultimatum game illustrates how human beings don't always maximise personal benefit rationally. It seems that we humans have a powerfully evolved sense of fairness. So powerful, in fact, that we would rather walk away with nothing than permit someone else to take extreme advantage of us. Researchers call this “altruistic punishment.”

[@centurion180ad]

@JimBobJenkins YOUR assumption is that Tommy will accept the 1 cookie offer with a 100% probability. In YOUR assumption the mother's second option may as well never have been offered, because you assume Tommy will only choose it 0% of the time. In other words this is no "game," because you have put the outcome into the given conditions. For my own personal part, it is obvious that I would say it's 50/50 or mommy can take the cookies away and eat all 12 herself.

[@spa9876]

What about a game where the girl gets to offer a deal. If the boy accepts the cookies are distributed as such. If he declines the amount f cookies are cut in half rounded up and he gets to propose a deal. Repeat this process until a deal is accepted or no cookies are left. What about if two cookies are subtracted each time a deal is rejected? What if there is a limit to how times deals can be proposed, then after the limit is reached, nobody gets any? What about a mix of these scenarios?

[@Gametheory101]

My homework set for this covers when two get taken away each time and when they both get to go back and forth for a certain number of offers. I will be covering these in future videos. But first we need backwards induction, which is something we haven't covered yet. Interestingly, though, when you cut in half or take away two each time, you get Rubinstein bargaining, which I alluded to in the video. Insightful thinking on your part.

[@Gametheory101]

@cmlspice We'll do that in the video with continuous offers. Here, while technically an equilibrium, it isn't a very sensible choice for Tommy, which is why we should not expect that outcome.

[@AugustasPalubinskasasas]

You speak like if Chatgpt was a human being

[@gucciv1]

you should mention (although maybe obvious) that the cookies are indivisible, because if not angelica can increase her payoff by dividing the offer by 2. In this case the only equilibrium is that tommy accepts all offers(including 0) in which case angelica gets 12 and tommy gets 0 (indifferent between the offer and the reject action)

[@geishaultra]

Exactly, I think 12:0 is also a Nash Equilibrium as Tommy has no better alternative, only one that is as good as what he is already getting. So if Angelica gets 12 or 0 doesn't matter because he's getting 0 either way, so there is no profitable deviation for Tommy.

[@Gametheory101]

@centurion180ad We can put whatever assumptions we want to in the model. I talk about this at length in a video later in the lecture series. But it is still very much incorrect to expect a 50/50 split here.

[@Cowtymsmiesznego]

What about a Nash Equilibrium where Angelica offers Tommy 8 and takes 4 for herself, and Tommy accepts if gets at least 8. It's not subgame-perfect, but why would that be necessary?

[@loneRambler]

There was a 2012 study done in China that used a modification of Ultimatum. Rather than making the players feel like each round started with an unallocated windfall, they made one of the players feel like it was their own money in the first place. The upshot is that players starting with the impression it was their money in the first place even rejected a 50/50 split 17% of the time. That is awful costly punishment, being willing to give up half of the windfall.

[@XBlackFlagX]

I was wondering if it was an assumption of game theory that actors are rational, or if at least some branches of it considers these problems with irrational actors. In reality, this situation sounds a lot like division of plusvalue into profit/wages, and we find that when a certain threshold of 'unfairness' occurs, people are willing to go on strike and gain 0 in order to cost a comparatively much higher value to their employer, as a strategy of negotiation.

[@centurion180ad]

This experiment is not a double blind, it is a negotiation, and the number of cookies involved is made available beforehand. The 2 parties must agree, or both lose everything, but Susie has the final word. Billy will play the probabilites of effecting a "fair" 50/50 split. A huge part of "happiness" is eqity. 1 to 11 split sucks. It is better that both get 0, because Billy only loses 1 but Suzie loses 11. She has the most to lose, and that is Billy's leverage.

[@centurion180ad]

@JimBobJenkins It is exactly the correct approach. "Hey sister, either I get half those cookies in a 50/50 fair split or YOU will lose ALL your cookies." Greedy sister stands to loose a heck of allot more, because she covets all the cookies save the 1 that she is willing to offer her brother by mom's rules. So the threat of loosing all is WORSE for the sister. Threaten the greedly little girl to loose all of her cookies, and she'll loosen up.

[@Esthefany91]

I watched your video the day before of my game theory final and this happened to be an extra credit question and I got it almost right!! He took points off because he asked if there was an equilibrium where both players receive an equal payoff, and I answered that there was an outcome where both players receive the same payoff, but it wasn't an equilibrium, and explained my reasoning; but according to him any outcome is an equilibrium, but (11,1) is the only subgame perfect :(

[@centurion180ad]

@JimBobJenkins The odious nature of the mother's favoritism working against Tommy, virtually guarantees that the sister is going to have a fight on her hands. IMO a "thinking" Tommy would use a honey and hammer approach. "Hey sister we split all these offers by mommy to you or to me 50/50 now and into the future. If you try to shaft me on this, this 1 time i'll burn the offer and we'll both get nothing." Sis will see the light! Run this experiment a thousand times, and get the average.

[@Hayleyfire929]

He's already stated that fairness comes in later. This is just a demonstration of a fundamental game theory logic. Hence, any moral or extraneous variables at play are assumed not to count.

[@geishaultra]

I think 12:0 is also a Nash Equilibrium as Tommy has no better alternative, only one that is as good as what he is already getting. So if Angelica gets 12 or 0 doesn't matter because he's getting 0 either way, so there is no profitable deviation for Tommy.

[@grfrjiglstan]

Before we had Lines On Maps, there were…Lines.

[@centurion180ad]

I do not follow this logic, because Tommy will obvioulsy threaten his sister that she will get NO cookies what-so-ever if she doesn't make a fair offer.

[@scrumsiparacetamol]

agreed with phillnoll. angelica has no actual power here, as tommy can just send her into the kitchen to bake more and more cookies.

[@philnoll]

There's something about maximizing my cookie intake that doesn't sit well with me. If people always played predictably according to this theory, you could get away with anything. But my decision would be based on fairness. If you get greedy with your offer, you may be punished.

[@philnoll]

That's a great analogy, and if you alone had won the lottery, I'd say its only fair to take the trip for 100,000. But for the sake of argument, who is in a better position to barter? I only stand to lose 100,000. But you stand to lose 4.9 mil. I can make an easy 2.5 mill out of it if I stay firm and let you watch the clock. And if you think I'm insane, that's even better. right?

[@philnoll]

@JimBobJenkins If you offered me 1 cookie, I'd reject it, and if we ever play again, you'd adopt a better strategy. In fact, I can turn the tables on you. I demand 8 cookies, or I will reject your offer. Basically its a battle of wills. After a few times getting nothing, we'd probably agree on 6 each.

[@wackinstack]

I think it would make more sense to offer 5 and keep 7. Over time, this would yield the most cookies in reality. Tommy would say yes every time and therefore Angelica would have a constant supply of cookies which is greater than tommy's. This way you have slow, steady growth without animosity. People work better together when they both benefit. it's a smarter choice. always go long term.

[@teamupleft7097]

Except that Angelica cannot reject the whole thing; only Tommy can. In iterated games Tommy can communicate an intention to reject any splits besides X=11 and X=12.

[@mensaswede4028]

Although it's true that the theoretical equilibrium is an offer of 1 cookie (as this video states), actual experimenters have run this experiment with real money and they discovered that the equilibrium for real human behavior is about 60/40, i.e. Angelica offers 40% of the cookies to Tommy and keeps 60% for herself. The reason the actual human behavior equilibrium differs from the theoretical equilibrium is hotly debated. Sociologists and economists have all weighed in on why Tommy typically rejects an offer of 1 cookie, when such rejection results in him receiving 0 cookies. What shouldn't Tommy take the one cookie, when his alternative is zero cookies? My preferred explanation is that Tommy knows the offer of 1 cookie is unfair, and chooses to punish Angelica for making an unfair offer (she will also receive 0 cookies when Tommy rejects her offer).

[@RedToilets]

That’s why this game fails. In real life, people sanction others for bad behavior even though it makes them worse off in the short term. They do this because they think that it’ll stop the person from engaging in the behavior in the future.

[@silkus]

If 10 other kids would witness what Angelica did. And any one of those 10 kids would get another 12 cookies, and she would be able to choose another kid that she would like to play the same Ultimatum game with (i.e. offer to share and get non if another person rejects). Please make a guess would the new kid choose Angelica as a play mate? What if every kid gets 12 cookies and have to play the game but can choose the partner. Would you choose someone that only looking for their own interest? What if the kids would get 12 cookies each and the game should be played multiple times but they could choose a different partner each time? It's more like a real life example. The correct answer is - everyone wanna play with the most generous kid first. So in the end, the one's that share - gets the most.

[@Gametheory101]

@centurion180ad That threat is not credible if Tommy wants to maximize his cookie output.

[@fionaNESS]

awkward, because in uni we were taught that angelica would offer 12 for herself, and tommy being indifferent would accept it :/

[@Gametheory101]

@centurion180ad That outcome does not follow from the assumptions given.

[@Mister.Psychology]

I didn't get it. Why is the stickman without a head? And where is his cool karate?

[@TheJaewhan]

but I guess that the assumption here is that Tommy does not have that chance of making a statement before his sister offers him an amount?

[@mrbigberd]

wrong conclusion. Logic dictates that you accept because something is better than nothing....BUT... the girl in the game would have a 10 cookie advantage. Therefore, it is better to accept nothing and retain equilibrium because equal is better than less than equal and equal is better than competitive loss. You have effectively paid one cookie to destroy 11 of your opponents cookies.

[@davidececchini5998]

This is the game theoretic backward induction solution of the game, but it has been proven this case never happens under any real life condition, where responders refuses most of unfair offers (I can say they will refuse any extremely unfair offer such as the 11:1 proposed in the example). I think the video is misleading because it misses the whole scientific debate from Güth et al. (1982) until now.

[@Croix1]

+Davide Cecchini this assumes perfect "rationality".

[@WavyCats]

@@Croix1 A rational person would not act like this, so it's not very rational at all...

[@Croix1]

@@WavyCats theres a reason i put it in quotation marks buddy

[@Paddy104]

wait.. im pretty sure its within any humans nature that unless they are offered something below 5 cookies will result in them telling the other to fuck off and they will happily suffer no cookies in order to see the other suffer no cookies aswell.

[@Gametheory101]

I try wherever I can.

[@SketchyHippopotamus]

that' under the assumption this game will ever be played again

[@mrgrehan9981]

dam rugrats..

[@hukslee]

The introduction of a "Mother" would make this game bayesian and I don't think you want to do that to yourself.

[@jonseidman1]

this explanation is fundamentally flawed...because in fact Tommy wouldn't, on average, accept 1 cookie, even though logically he'd be better off...but he'd only be better off in the VERY short-run, not in the long run. in the long-run, he'd be better off 'punishing' Angelica in the short-run, so that in the future she will offer a fairer share. because if he doesn't 'punish' her, she's just going to keep offering 1 cookie every time. Scenario A: T accepts 1 cookie Game 1: A offers 1 cookie. T accepts it.......Total cookies for T = 1 Game 2: A offers 1 cookie. T accepts it.......Total cookies for T = 2 (1+1) Scenario B: T rejects 1 cookie Game 1: A offers 1 cookie. T rejects it.......Total cookies for T = 0 Game 2: A offers 6 cookies. T accepts it....Total cookies for T = 6 (0 + 6) You can see that this explanation only works for 1-off events, and even then you can argue that although it is a 1-off event in the lab, the participants wouldn't be able to disconnect it from the fact that the outcomes have an effect beyond the lab... Which, in a society, they invariably would....Because you'd invariably run into A again. Clearly, rejecting the offer of 1 cookie is the most logical and rational thing to do when looking at the long-run.

[@Gametheory101]

That's addressed here: kzbin.info/www/bejne/qnjGmGptrtdnnqs You would think it would work out that way, but it doesn't. Basically, you need the ability to make offers before you can actually capture surplus for yourself,

[@FBIRyan]

William Spaniel In real-world practice it does work out as how Jon describes. Even in lab Ultimatum Game experiments with 1-time offers people often rejected when proposed less than 30%. People aren't 100% rational beings, they're social beings that value fairness. The interesting part is how their perception of value can be altered and thus subjective fairness.

[@genuinepetermorgan]

this is clearly a one shot game, just as in Andersen's 2011 paper, so talking about the long-run is a waste of your time, a waste of anybody's time who has read your comment, and a waste of my time for replying. Please think more before commenting next time

[@FBIRyan]

***** Thanks for replying and wasting my time talking about wasting time.

[@genuinepetermorgan]

strong chat

[@nhlhammy]

I like the video, I know that in practice the scenario described does not hold up in most cases but I also know that the ultimatum game is only a model that cannot describe the real world entirely. What I found more bothering is that, since this game is based on standard economic theory, it is left out there there actually is more that just the (11,1) equilibrium described in the video. Talking strictly theoretical the allocation (12,0) is an equilibrium since Tommy still cannot be better off from choosing reject. As many have said before and what I agree with is that the theoretical aspect of the game mostly doesn't hold in practice, because there are boundaries to human's rationality (as defined in standard economics) and egoism. Personally, I think it is natural for a human being to show some sort of social goodwill and in that to avoid completely unequal allocations. Outside the theoretical framework, A would usually not propose a split as unequal as (11,1) and Tommy would not accept it.

[@rumpusRoom_]

I'm pretty sure that Angelica will play x=0. EDIT: Sorry I'm quite wrong. I didn't got that the cookies were a nod for a discrete game. Cheers.

[@yaleha07]

So do the cookies belong to Angelica? Is she trying to get something from Tommy? What if he takes the 5 cookies just to have some but doesn't follow up on his commitments since he believes the split was unfair? Game theory is great at all but ultimately its nothing but bullshit.(the ideas behind it are as old as time itself, i can't believe certain people actually got a noble prize for "coming up" with all this" It all comes down to being able to enforce your will

[@MelissaTem]

very well explained ! Thanks

[@Gametheory101]

Never watched Rugrats, did you? :)

[@stephenschumacher7876]

Lesson 1 on why capitalist market incentive structure results in such variance of wealth distribution. 😝 nice video.

[@hollister2320]

Your Game Theory videos are as relevant today, during the Ukraine War, as they were the first time I saw them William-13 years ago🤧! it’s all coming full circle man

[@centurion180ad]

Game Theory as presented in this video, is an excercise in logic & math, but somehow they end up ignoring anything remotly resembling sane boundary conditions. Game Theory as you have explained it, is political theory.

[@kikazz91]

lol are all of the names in your videos cultural references?

[@centurion180ad]

This game is rigged by the "mother's rules," before it ever gets started. If I was "Tommy" i'd reject the game in the first instance. I'd tell mommy, keep your cookies and jam them up that shoot where the sun never shines. Sister can go cry in her beer, that life isn't fare some more, boo hoo hoo.

[@centurion180ad]

Attorneys & lawyers play these silly sack-of-horse-apples mind games their entire stinking lives. What is a purpose of defining an arbitrary set of rules, for explicit purpose of creating yet again another set of arbitrary boundaries? If your game does not model or predict anything SANE, then you are in a position of circular logic, of having forced an outcome that you decided beforehand. IF you say "billy MUST choose," then it is not a choice, it is a fiat command devoid of sanity.

[@22thejew]

rugrats!!

[@staybased9320]

a propagandist was born

[@SteveInLava]

Everyone will know you're a troll account lol