Several studies have found that first-born children do better in school. The perplexing part is why this happens. Is it because the first-born child has no one to learn from? Is it because the first-born child gets the parents’ full-attention while others have to share it? Or maybe it’s because first-born children have higher IQs?

None of these answers has been wholly convincing. And a new study considers an alternate explanation that parents might be responsible for the pattern. The theory is that first-born students do better in school because they are putting forth more effort. And the reason for that is parents are stricter on first-born children. Why? The answer is based on game theory: the parents are strict on the first-born in order to develop a reputation for being tough.

The economists V. Joseph Hotz and Juan Pantano support this idea by analyzing school performance of children between the ages of 10 to 14. They find that the first-born kids tend to do better in school and parents are tougher on them in terms of monitoring homework study time, limiting distracting activities like TV, and handing out punishments for poor performance.

The study is definitely worth checking out. Below I describe a bit about the game theory model used in the paper.

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"All will be well if you use your mind for your decisions, and mind only your decisions." Since 2007, I have devoted my life to sharing the joy of game theory and mathematics. MindYourDecisions now has over 1,000 free articles with no ads thanks to community support! Help out and get early access to posts with a pledge on Patreon. .

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Game Theory Model

Before getting to strategic parenting, consider first the following textbook example. A monopolist controls all the profits for a market (payoff of 1). But a new company is thinking about entering the market, and if it is successful, it would split the profits (payoff of 1/2 to each). The monopolist threatens the new company that if it enters, it will engage in a price war so fiercely that both companies would eventually get hurt (payoff of -1/2 to each). This is in hopes that the new company does not enter the market, and the monopolist retains its full profits.

What will the new company do? In this simple model, it is easy to see the monopolist’s threat is completely hollow. If the new company enters the market, the monopolist would much prefer to split the market (payoff of 1/2) than to fight it out (payoff of -1/2). Therefore, the company enters the market and the monopolist has to acquiesce.

What if another company then wishes to enter the market? The game tree gets bigger–and I won’t draw it out–because the logic is exactly the same. While the monopolist might threaten a price war to keep out the entrant, the threat is not credible and the new company can safely enter, knowing the monopolist will acquiesce.

Similarly, if a monopolist faces a set of N sequential entrants, the solution, found by backwards induction, is that each company will choose to enter the market, and the monopolist always acquiesces every time.

This is a puzzling solution. The monopolist seemingly would be better to fight a few early entrants to ward off future ones. Furthermore, in reality, companies do fight new entrants and they do try to deter potential competitors from entering the market. How can we explain that?

This is where the Kreps-Wilson entry deterrence model is useful (You can read Reputation and Imperfect Information for the details, I offer an intuitive explanation in this post. As I understand it, Paul Milgrom and John Roberts independently developed a model of predation and entry deterrence in 1982. More on that in Predation, Reputation, and Entry Deterrence. This post will discuss the Kreps-Wilson model).

The Kreps-Wilson model considers the same monopolist game, except it allows for the possibility of two types of monopolists: one that is weak and does not wish to fight, and another that is strong and relishes in fighting. The strong monopolist’s type changes the outcome of the game: since the monopolist prefers fighting, the new company is much better off staying out of the market.

The new company wishes to enter if the monpolist is weak, and it will stay out if the monopolist is strong. The hitch is that the entrants don’t know the monopolist’s type. They have to make an educated guess based on things the monopolist does. In technical terms, they will guess the monopolist’s type based on its behavior, updating their beliefs using Bayes rule, and choose to enter or stay out depending on which has a higher expected payoff.

There is another important part of this game. A strong monopolist will always prefer to fight. So if ever a monopolist chooses to acquiesces to a company, that must mean the monopolist’s type was weak. Therefore, all future entrants learn the monopolist was exposed as weak and they will enter the market without fear of a price way. The question to this game is: what’s the best way for a weak monopolist to play, and how will the entrants respond?

The answer is described in the equilibrium, known as a sequential equilibrium. The strategy for the strong monopolist is simple: fight every time. The interesting part is the strategy for the weak monopolist. While the weak monopolist never prefers to fight in any given round, it can actually profit by fighting in early stages. The entrants will then be unsure if the monopolist is weak or strong–in other words, fighting will create a reputation that the monopolist is actually strong. The cost of fighting a few rounds can then be made up by the profits in subsequent rounds as competitors stay out of the market entirely.

So what does any of this have to do with parenting? The economists V. Joseph Hotz and Juan Pantano considered raising children as a sort of sequential Kreps-Wilson entry deterrence game. The parents play the role of the monopolist that can either acquiesce or discipline in response to bad behavior. The child plays the role of the new company that can either behave (and avoid confrontation) or can challenge and see what the parent does.

In this game, there are two types of parents. A tough parent is going to be strict and always take the effort to punish their children for poor effort. A lenient parent hopes the child does well and avoids confrontation if possible. The order of birth of the children is akin to the sequential nature of the entrants to the market: the first-born child is like the first entrant. What should strategic parents do in this game?

The solution to Kreps-Wilson model suggests that lenient parents will try to be stricter early on–to the first-born child–in hopes that it creates a reputation so their younger kids just put forth effort. Or put another way, the parents will be strict with the first-born, even though they don’t like it, to avoid revealing to the younger children that they are lenient.

In the final stage of the game (the youngest child), the lenient parents have no reason to be tough for reputation. They can choose to be lenient, and thus the younger child might be more inspired to put less effort in school.

The result of the model is that first-born children end up with stricter rules and more punishments, resulting in more effort in school and higher performance.

Remarkably the equilibrium of this game is consistent with the data the study authors found in a longitudinal study of 10-14 year olds.

(And in conclusion, a tangent about the study. I think the model reveals something about American culture. My initial reaction based on my Indian upbringing was, “What the heck is a lenient parent?”)

Another tangent: misleading headlines

My friend sent me an article about this study. I am always thrilled when economics or game theory makes gets covered in popular press. But I get really frustrated that headlines are chosen to be controversial instead of accurate.

One of the first articles was in The Atlantic:

The study in fact did not directly claim first-born children are SMARTER. It discussed this idea in its literature review. But the study was actually about school performance, not being “smarter.”

The danger in this headline is that it gets parroted in other media (either that or the other journalists also found a way to get the study wrong).

Here’s about the only headline I found that stated the results more accurately:

Science World Report: Strict Discipline Helps First-Born Kids do Better in School

Is it too much to ask journalists to be accurate in their headlines?

References

Strategic Parenting, Birth Order and School Performance. V. Joseph Hotz and Juan Pantano. NBER Working Paper No. 19542. October 2013

Kreps, David M. & Wilson, Robert, 1982. Reputation and imperfect information, Journal of Economic Theory, vol. 27(2), pages 253-279, August.

Paul Milgrom & John Roberts, 1980. Predation, Reputation, and Entry Deterrence, Discussion Papers 427, Northwestern University, Center for Mathematical Studies in Economics and Management Science.”