Game Theory and Child-Rearing

A reader named Clark Case, who lives in Aurora, Ohio, and works as a product manager, writes in with a child-rearing observation. His kids are 7 and 4; his wife is a homemaker:

My wife came up with a punishment method for my kids that I thought that you (and perhaps your blog readers) would find interesting.

When the kids get to tussling and or screaming at each other in such a way that she is finding aggravating, she will send them to their respective rooms with the stipulation that they can come out when they both agree to apologize to each other.

Game theory, I suppose, would argue that they should immediately apologize to one another to minimize the period of detention. What seems to happen, though is that one will think that the other deserves some extended detention and will give up freedom himself in order to see that the other gets it.

Am interested to hear other game-theoretic attempts at child-rearing …


I used to think this was more unique, but have since read and heard of other parents employing this technique.

Whenever my brother and I had to share some sort of food, one of us would be given the task of cutting, and the other could then choose which half he wanted. Whoever did the cutting would then be extra careful to cut it exactly in half.


Once the kids figure out that the apology can be insincere, game theory over.

Craig French

I too have noticed this gaming with our kids to a limited degree.

I noticed a tangential effect I think of as a "peer-induced performance-muting effect": One example is -- our 11yo daughter and 10yo son both took piano lessons from the same teacher, and little brother really excelled. Big sister became vocally disheartened at her brother's surpassing her skill level and eventually stopped lessons entirely. In response, our son also slowed way down and became less enthusiastic about sitting down at the keyboard at all, and I suspect this reaction was in empathy for his sister's "plight".

I think this effect also exists in sports teams to some degree -- unless a player has a very stong performance advantage over his teammates and can't help but show it (Sidney Crosby, etc), teammates tend to herd in their demonstrated abilities in practices and games, regardless of meaningful, though not outlier level, skill differences -- anecdotal evidence from observing the same 2 kids playing youth sports.


Ian Kemmish

Is this a game theoretic attempt at child rearing, though? The mother surely can't be either expecting or worse hoping, that the children will agree straight away and thereby escape punishment, so it seems clear that she has developed this method in either innocent or wilful ignorance of this aspect of game theory. So, whatever the basis for the approach is, it isn't game theory.

Douglas Warren

I think that is just pure, sibling spite coming into play.

Mike L

Whenever my kids (7 and 5yr old twins) argue over a toy, I put the toy in a timeout and nobody can play with it. They get it back when they agree on a solution for taking turns. Their negotiations are fascinating.


Your theory is flawed. They are not "giving up" freedom or anything else. Your assumption is that being in their respective rooms is the same as giving up freedom. But, they haven't given up anything -- they're just in their respective rooms doing something else.

Jennifer Tamez

I make mine (3 and 6) put their noses to the wall, but separated so they can't taunt each other. I don't put any conditions on it. I don't tell them they have to apologize. I just wait to see what happens. Somehow within 2 minutes, they are calm and ready to resume play in a cooperative manner.
Do you think the lack of conditions is what changes the scenario?


@Craig French

I think a simpler name for your "peer induced perfomance muting effect" would be "competition". I would suspect that without the drive to outdo big sis, your son's desire to excel is diminished.

I have noticed the same effect in sports also. In teams that have a higher level of skill, a skilled but lower level of player will drive himself to improvement. On a less skilled team, the same player can excel in the peer competition without exhibiting the a higher level of personal drive. - anecdotal evidence from observing my six boys in sports and life.


Our kids played upstairs in a bonus room. If I heard fighting I'd go upstairs and break it up, then proceed to find all kinds of things that needed to be cleaned. The bonus room was always a mess.

It didn't take many iterations of that process before I started hearing fighting, then "shhh! Do you want dad to come up here and tell us to start cleaning up?!"

Problem solved. Behavioral economics to the rescue.

A friend who now has young kids uses the same technique on his children after I told him that story. He says it works like a charm.


@Craig French, it's possible that your son never enjoyed piano, he enjoyed being better at something than his elder sister. instead of displaying empathy, it is conceivable that piano (to him at least) is like any competitive activity, not worth doing if the competition doesn't try.

It could be Important to include into the game that one or both of the children might understand that repeated instant solutions might lead to a more severe punishment. This has the result of the time it takes is what they perceive to be the minimum acceptable (to the parent) punishment rather than just the least possible time. (it is after all an infinite turn game)


Father in question here - I saw a parallel in my kids behavior and in the experiment where two parties can share a dollar if party 2 agrees with party 1's plan for splitting it.

Game Theory would suggest that party 2 would agree if they are given even a penny, but actual execution of the experiment shows that party 2 rejects the split if they aren't given a more "fair" share.


There are too many problems with this attempt. The cognitive abilities of children of different age are very different and so is their ability to calculate or predict the outcome. All that is assuming the choices kids make are rational. However, any parent probably observed irrational behavior of their kids at different times (for whatever reason). This irrational behavior is especially noticeable during the conflicts. Giving all that I'm just not sure if game theory approach to correct behavior problems in kids is any good. Maybe behavioral economics or better yet psychology is more direct approach.


Part of the premise of game theory is that you need two rational actors capable of weighing short-term and long-term outcomes. Do we honestly think that a 4 year old and a 7 year old are capable of such reasoning?


Well, I used some form of game theory, I suppose, to find out which correction my son hates the worst. I was planning on grounding him, but he said, "Can you spank me instead?"

Of course, I don't like to spank him, and now I had found out that he hated being grounded worst of all. Which meant, of course, that I immediately grounded him.

In another usage, I tell my son that there is just "no way" he could be as smart as me...which ensures that he will now do his homework with a vengeance, to prove ol' Dad wrong. He doesn't realize that I am "playing" him, using strategy to get him to do what I want him to do.

Of course, he plays his games too. Like the time he said, "Daddy, when I have kids, if they want to play, I'm going to get off the computer and play with them right then. And when I ground them, I going to only ground them from TV and the internet--they can still play with their toys."

So now I don't ground him from at least one toy...and I get off the internet when he wants to play.

Oddly enough, I don't feel like I "lost" at all!



When this used to happen in my house, one child - me or a brother - would actually want some time alone and the punishment enabled that. Don't assume siblings always want to play together; they get tired of each other. I would first assume that one child simply prefers to be alone for a while, maybe playing at his own imaginative games. The idea that the child intends to punish the other is an adult interpretation which substitutes the complicated for the simple, that a young child - assuming these are young kids - acts toward another rather than for his or her own interests.

Remember that children expect squabbles in all their relationships and that well -adjusted children don't hold them against others the way adults do. Young best friends fight. Let's say they intend some form of punishment or vengeance. That would mean fighting of the normal sort has consequences and that would tend to negative results because children rationally prefer not having consequences affect their play decisions. Why play with this person if fights lead to punishment? Again, adults do this: they fight and they remember and they hold it against each other and they get divorced or stop talking to each other.


Chad the Tutor

Quite literally, the classic Prisoner's Dilemma.


There might be another factor for the "prolonged" detention: the kids can be so much tired with each other to want to stay alone for 15 minutes.


@ Ian Kemmish, #4: My guess is the mom's goal is to get the kids to stop fighting, not to punish the kids. The punishment is merely one way to achieve the goal.


This is not a one shot game, but a dynamic one, namely one can model it as infinitely often repeated, since the kids live together and so interact on a daily basis. In a one shot game it would be rational to forgive immediately, but in a dynamic setting it can be advantageous to punish, even if it's costly, in order to avoid future "defaults" from other players.