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Game Theory × Identity

The Boy Who Solved the Nash Equilibrium

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The Boy Who Solved the Nash Equilibrium

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13 min read

Five Scenes on Suffering as Proof of Worth

Psychoanalysis × Game Theory × The Economics of Signaling

By Oscar Rey de Castro, Psychoanalyst — IPA Member

Clinical note: This essay is a cultural and interdisciplinary analysis. It does not constitute psychological diagnosis, prescription, or therapeutic treatment.


A boy finishes his homework in four minutes and runs off to play. His father — director of a company — scolds him.

That same afternoon, in his office, that same father complains to a colleague:

"My employees overengineer everything. They never get to the point."

He demands more effort than the job requires from his son. He demands less from his employees.

If his son were his employee, he'd fire him for working the way he demands his son work. If his employee were his son, he'd praise him for working the way he can't stand his employees working.

One complaint runs on moral logic. The other on economic logic. Nobody notices they're the same complaint, said in reverse.

Three different disciplines explain why that contradiction makes you uncomfortable — and why you don't see it.

Game theory: in many strategic situations, the optimal play isn't the one with the most effort. It's the one with the right effort. The boy who finishes in four minutes isn't being lazy. He's playing well.

The economics of signaling: the father isn't asking for results. He's asking for a visible sign of commitment. When what matters can't be measured directly, visible suffering becomes currency. Sweat as proof.

Psychoanalysis: underneath the other two, there's something older. What the father repeats with his son is what someone else repeated with him. A transmission that doesn't know itself.

Same boy. Same four minutes. Three ways of looking at what you're doing when you scold him.


1. The Equilibrium

There's a field of knowledge that studies precisely this kind of situation. It's called game theory. And one of its most counterintuitive insights is this: the best strategy rarely consists of doing as much as possible. It consists of doing what's necessary to obtain the best result given the constraints.

A boy who finishes a task correctly in four minutes and redirects his energy toward play is solving, in his own way, an optimization problem. He meets the external demand at the lowest cost. He preserves energy for an activity of higher subjective value.

In a boardroom that would be called efficient resource allocation. In a classroom it gets called lack of effort.

John Nash proved that in certain interactions there exists a point of equilibrium where no player can improve their outcome by changing strategy unilaterally. In the dynamic between a boy and his school, that equilibrium is revealing.

If the boy does less than required, he gets sanctioned. If he does exactly what's required, he gets the expected result. If he does much more, he doesn't always get much more. The grade has a ceiling. The extra recognition is marginal. The time invested, on the other hand, is gone.

From that logic, the "minimum" isn't necessarily a failure. It can be the precise point where the demand is met without wasting energy.

But here a decisive distinction is needed.

Not every minimum effort is efficiency. Sometimes it's avoidance. Sometimes anxiety, apathy, opposition, an attentional difficulty. Sometimes it's an early renunciation of the desire to learn. The point isn't to romanticize indifference. It's to stop reflexively confusing efficiency with moral defect.

There are tasks of compliance, where excess is waste, and tasks of formation, where what looks like excess is the practice itself. Confusing the two is what produces the complaint.

The problem isn't the boy's strategy. The problem is that many adults only recognize value when it comes wrapped in difficulty.

"He works hard" reads as good, even when the result is mediocre.

"He finishes fast and goes off to play" reads as suspicious, even when the result is correct.

We have confused suffering with seriousness.

But an equilibrium solves a problem. It doesn't explain why the problem was badly posed in the first place.


2. Sweat as Costly Signal

Michael Spence won the Nobel Prize in economics for an idea he thought was about the labor market but that ends up explaining half of everyday life: when two people can't directly measure what matters, one of them sends signals. And for the signal to be credible, it has to be expensive.

The university degree, in Spence's classic reading, doesn't necessarily make you more productive. But completing it signals that you're the kind of person who can complete it. The signal works because it costs something. A lazy person wouldn't make it to the end.

The father watching his son finish the homework in four minutes isn't reading the result. He's reading the absence of a signal. There was no sweat. No tears. No "dad, help me."

The father interprets efficiency as lack of proof — and lack of proof as lack of commitment.

That logic governs the office.

The consultant who stays until ten didn't necessarily work more. But he sent the signal. The employee who answers emails on a Sunday at eleven at night wasn't necessarily more productive. But he established his type.

The hustle culture is signaling theory applied without anyone calling it that: working eighty hours not because it's necessary, but because the visible hour has become the currency you use to buy the trust of the person who decides your next bonus.

The father who scolds the efficient son and the boss who rewards productive inefficiency are the same person, in two contexts where the currency of payment isn't the same.

In the classroom, sweat gets paid. In consulting, results get paid — but sweat keeps cashing in a little more.

So the father raises a son trained to send expensive signals. And thirty years later he's surprised to find that his son, now an employee, overengineers everything.

It's exactly what he taught him.


3. The Oscillation

The argument isn't "let kids do the minimum." That would be as simplistic as the complaint it's trying to dismantle.

The interesting thing is what happens when the same boy closes the notebook.

Watch a child in free play. Not the one in a structured after-school program. Not the one playing something an adult designed for him. The one sprawled on the floor with blocks. Or making up a story with little figures. Or building an entire world with erasers and paper clips.

That child is giving himself over with total intensity. Not because anyone is demanding effort. Because the activity calls him in.

He loses track of time. He ignores the adult who calls him to dinner. He plunges in with a concentration no teacher has ever managed to demand of him.

The same child who "does the minimum" on the homework is capable of absolute immersion in play. He doesn't lack the capacity for effort. His organism distinguishes — with a precision that we adults have lost — between what deserves total surrender and what deserves efficiency.

Donald Winnicott wrote in 1971 a sentence that psychology still hasn't finished digesting: "It is in playing and only in playing that the individual child or adult is able to be creative and to use the whole personality."

Play isn't rest from real work. It's the space where the self is constituted. The child who plays is doing the most serious work there is: he creates reality, tests limits, invents rules, breaks them, repairs them. He discovers what he can control and what he can't. He experiments with versions of himself without getting permanently fixed to the consequences.

Play isn't the opposite of effort. It's effort in a free state.

That's why it's so impoverished to treat it as a reward.

"Finish your homework and then you can play."

The sentence sounds reasonable. It hides a problematic inversion: it turns play into a reward that comes after work, when play is the most important psychic work of childhood.

Thomas Ogden, rereading Klein, proposed thinking of psychic experience not as a sequence of stages one moves past, but as an oscillation between modes of organizing reality. The paranoid-schizoid position fragments, categorizes, protects. The depressive position integrates, contextualizes, repairs. Neither one is enough alone. The living mind oscillates — though in clinical work the boundaries between those modes are more porous than any tidy summary allows.

The child who does the minimum on the homework and then plunges three hours into an invented game is oscillating well. Economy when the task doesn't call him in. Immersion when something captures him.

The broken adult applies a single rule to everything: try harder. He doesn't distinguish contexts. And by not distinguishing, he teaches the child to stop distinguishing too.

What the office rewards thirty years later isn't constant effort. It's discernment — knowing when to push and when to conserve. That capacity is built in exactly the oscillation the adult interrupts.

And there's something else.

When a child invents a game with others, he isn't "wasting time." He has to imagine what the other wants. What the other knows. What the other believes. What the other can tolerate. He has to regulate impulses, take turns, modify strategies, sustain a shared fiction. Peter Fonagy called mentalization that capacity to understand behavior in terms of mental states. It isn't learned by completing worksheets. It's trained in ambiguous situations, in scenes where the child has to read the other without erasing him.

We want adults with initiative, but we train children to obey instructions.

We want creative adults, but we're suspicious of unprogrammed time.

We want adults capable of deciding, but we punish efficiency when it doesn't come wrapped in a visible expression of effort.


4. What Gets Transmitted Without Anyone Meaning To

There's a circuit that reproduces itself with a silent efficiency.

School teaches the child that visible effort is virtue. The child grows up and becomes an adult who doesn't know how to calibrate his investment of energy. He works twelve hours not always because it's necessary, but because he needs it to show. His boss complains about his inefficiency. That same adult comes home and demands visible effort from his son.

The cycle restarts.

The expensive signal Spence described for the labor market has become, without anyone noticing, the emotional language of parenting. The father isn't asking for results. He's asking for a performance of suffering that confirms to him that his son is taking things seriously. And when the boy solves it fast and goes off to play, the absence of signal is read as absence of value.

Sandor Ferenczi, the Hungarian analyst who was the first to systematically study relational trauma in children, described in 1933 a mechanism he called identification with the aggressor. When a child is subjected to a pressure he can neither process nor confront, he can end up incorporating the logic of the one who's pressuring him. He doesn't just obey. He learns to call invasion love, humiliation teaching, hardening character.

Decades later, sitting across from his own son, he repeats the same violence in pedagogical version.

"That's how life is."

"They demanded things from me too and I turned out fine."

"You'll thank me later."

But something did happen. What happens is that often what got broken was confused with maturity.

Clara Mucci has shown how early relational trauma isn't transmitted only as memory, but as a way of being in the world. What gets inherited isn't a scene. It's a position. A way of understanding the bond, the demand, the body, the pain, the authority.

But here there's a fundamental distinction.

Not every demand is trauma. Not every limit is aggression. Not every father who asks for effort is repeating a violence.

There's a difference between teaching a work ethic and identifying with the aggressor. And the difference isn't always visible from outside.

The father who teaches a work ethic holds the ambivalence. He demands, but he registers the cost. He asks, but he watches the child. He knows that learning involves frustration, but he doesn't turn frustration into a cult. He can say: "This is hard, and even so it's worth it." He doesn't enjoy his son's submission. He doesn't need to see him suffer in order to feel calm. He tolerates the conflict of demanding without ceasing to care.

The father identified with the aggressor has lost that ambivalence. He doesn't register the cost because registering it would force him to remember his own. So he denies it. He calls it preparation for life. He covers it in hard phrases. Sometimes he even presents it as love.

From the outside, both scenes can look the same: an adult asking for effort.

From the inside, they're opposites.

In one, the child internalizes judgment. In the other, he internalizes submission. And that difference isn't easily caught by a parenting manual. Clinical work, on the other hand, lives off hearing those differences.

In the logic of signaling, the difference is this: the father who teaches a work ethic teaches his son to produce value. The father identified with the aggressor teaches him to produce expensive signals of value — sweat, visible difficulty, exhaustion — whether or not there's anything real behind them.

Thirty years later, the office is full of adults who no longer know whether they're working or acting like they're working.


5. The Girl with the Paper Clips

I return to the consulting room.

The father who complained is still sitting across from me, waiting for me to tell him how to fix his son. He wants a technique. A phrase. An intervention.

But I'm looking at something else.

I'm listening to the story this father carries without knowing it. The voice of his own father. The teacher who shamed him. The school that confused obedience with thinking. The company that rewarded him for staying late even when he wasn't producing anything anymore. The whole system that taught him that sweat is the proof of value.

And I'm thinking about the girl who finished her worksheet in four minutes and spent the rest of the hour building a kingdom out of erasers and paper clips.

Maybe she isn't failing.

Maybe she's doing what her organism knows how to do: meet the demand, preserve the surplus, invest it where there's still play.

But her father is going to come home. And he's going to scold her for not trying harder. And the girl is going to learn, slowly, that next time she has to take longer with the worksheet. She's going to learn to produce sweat. She's going to learn that the kingdom of paper clips doesn't count — that only what gets seen counts.

And thirty years later that girl is going to be sitting in an office, overengineering a memo, sending expensive signals to a boss who demands them, no longer remembering what it was to build a world in an hour.

The father who scolded her is going to be sitting in another office, complaining about his employees who overengineer everything.

The two complaints are going to be the same complaint. Said in reverse.

And nobody is going to notice.

Again.


Want to go deeper?

At The Crossover Project we care about the rigor behind the mix.

On the equilibrium nobody sees

Nash, J. (1950). Equilibrium points in n-person games. Proceedings of the National Academy of Sciences, 36(1), 48-49.

Three pages that changed economics.

On sweat as signal

Spence, M. (1973). Job Market Signaling. Quarterly Journal of Economics, 87(3), 355-374.

The paper that showed that in markets with asymmetric information, what counts isn't always productivity — it's the costly signal that demonstrates it.

On play as serious work

Winnicott, D. W. (1971). Playing and Reality. Routledge.

The book that demonstrates that to play isn't to rest from work — it's the most serious work there is.

On the oscillation between positions

Ogden, T. H. (1988). On the Dialectical Structure of Experience. Contemporary Psychoanalysis, 24(1), 17-45.

On mentalization

Fonagy, P., Gergely, G., Jurist, E. L., & Target, M. (2002). Affect Regulation, Mentalization, and the Development of the Self. Other Press.

On identification with the aggressor

Ferenczi, S. (1933). Confusion of Tongues Between Adults and the Child.

On intergenerational transmission

Mucci, C. (2018). Borderline Bodies: Affect Regulation Therapy for Personality Disorders. W. W. Norton.


What is The Crossover Project?

This article is part of The Crossover Project — a space that takes the logic of the video-game crossover and applies it to human thinking. We take ideas from fields that don't usually talk to each other — psychoanalysis and game theory, economics and child development — and force them into the same room. Each collision is designed to make you see something you hadn't seen.

We aren't looking for comfortable synthesis or a single truth. We're looking for friction.

We don't claim to resolve life's contradictions. We learn to hold them.

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MEDICAL DISCLAIMER // NOTA CLÍNICA
El propósito de The Crossover Project es estrictamente la disección cultural e interdisciplinaria. Estos ensayos exploran la mecánica del comportamiento y la fenomenología pop a través del lente del psicoanálisis, pero no constituyen bajo ninguna aserción un diagnóstico, prescripción ni tratamiento terapéutico individual. La lectura de este archivo no sustituye el rigor del espacio clínico ni la consulta profesional directa.