Stable Outcomes and the Limits of Stability

Hello again. In the previous lesson, you practiced forecasting another person’s likely move by reconstructing their goals, constraints, information, and assumptions. That perspective switch is the essential first step. This lesson adds a second question: if everyone has made a choice, would any one person want to change their own choice while everyone else stays put?

This is the idea behind a stable outcome, usually called a Nash equilibrium. It is one of game theory’s most useful concepts, not because it tells us what outcome is fair or desirable, but because it distinguishes a situation people can individually escape from from one they are individually “stuck” in. Those are very different things.

By the end, you will be able to inspect a simple interaction, identify an outcome where no participant benefits from changing course alone, and explain why that outcome may still be disappointing for everyone involved.

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Stability means “no profitable solo change”

Imagine that two colleagues, Aisha and Ben, are deciding whether to contribute useful documentation to a shared internal project.

Each has two choices:

• Contribute: spend time documenting their part of the system.
• Hold back: save that effort and hope to benefit from the other person’s documentation.

Suppose the outcomes are represented by rough “benefit scores.” Higher is better.

	Ben contributes	Ben holds back
Aisha contributes	4, 4	0, 5
Aisha holds back	5, 0	1, 1

The first number in each cell belongs to Aisha; the second belongs to Ben. These scores are not objective measurements. They summarize a mix of effort, time saved, quality of work, and access to shared knowledge.

Consider the bottom-right outcome: both hold back, receiving $1,1$.

Would Aisha improve her own score by changing alone to contributing, while Ben continues holding back? No. Her score would fall from $1$ to $0$.

Would Ben improve by changing alone? Again, no. His score would also fall from $1$ to $0$.

So “both hold back” is stable in the specific game described by this table.

A stable outcome has this test:

Holding everyone else’s choices fixed, no participant can improve their own outcome by changing only their own action.

This does not mean that people are delighted, morally justified, cooperative, or unable to imagine a better arrangement. It means only that a solo switch is unattractive.

The formal name is Nash equilibrium, after mathematician John Nash. For this course, treat it as a practical label:

Nash equilibrium: a pattern of choices in which each person’s current choice is a best response to the choices the others are making.

“Best response” is deliberately local. It asks, “What is best for me given what the other person is doing now?” It does not ask, “What would be best if we could redesign the situation together?”

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Read a payoff matrix as a set of conditional comparisons

A payoff matrix can look more technical than it is. It is simply a compact way to list the possible combinations of choices and their consequences.

The key discipline is to analyze one person at a time, while keeping the other person’s choice fixed.

Use this four-pass method:

1. Pick a participant. Look only at their outcome in each relevant pair of cells.
2. Assume one fixed choice by the other participant. Compare the first participant’s available options under that condition.
3. Mark their best response. It is the action that gives that participant the better result.
4. Switch perspectives. An outcome is stable only when every participant is playing a best response at the same time.

Return to the documentation example. Suppose Ben holds back. Aisha compares:

• Contribute: $0$
• Hold back: $1$

Her best response is to hold back.

Now suppose Aisha holds back. Ben compares:

• Contribute: $0$
• Hold back: $1$

His best response is also to hold back. Their choices meet in the “both hold back” cell, making it a Nash equilibrium.

But now look at “both contribute,” with $4,4$. It is better for both people than $1,1$. Why is it not stable?

If Ben is contributing, Aisha can personally raise her result from $4$ to $5$ by holding back. Ben can make the same calculation. So either person has an incentive to leave the mutually productive outcome, provided they expect the other person to keep contributing.

That is the central tension: an outcome can be better for everyone together but vulnerable to a tempting individual deviation.

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Watch the method once

A useful distinction from the video is between two related ideas:

Idea	Meaning	What it tells you
Best response	The best action given a particular action by someone else	A conditional choice
Nash equilibrium	Everyone is playing a best response simultaneously	A stable combination of choices
Dominant strategy	An action is best no matter what the other person does	A particularly strong reason to expect that action

A dominant strategy is not required for a Nash equilibrium. Some stable situations depend closely on what the other participant chooses. But when each person has a dominant strategy, the resulting outcome is especially hard to escape through individual action.

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The classic trap: stable and worse for all

The Prisoners’ Dilemma makes the distinction between stability and quality unusually clear. The image below uses prison years as the outcomes, so lower numbers are better.

At “both confess,” each prisoner receives 5 years.

• If Prisoner B confesses, Prisoner A compares confessing for 5 years with remaining silent for 20 years. Confessing is better.
• Symmetrically, if Prisoner A confesses, Prisoner B is better off confessing too.

Therefore, both confessing is stable. Neither prisoner wants to become the only person who stays silent.

Yet both prisoners would prefer “both remain silent,” where each receives 1 year. The problem is that this better joint outcome cannot be maintained by individual reasoning alone. If one prisoner expects the other to remain silent, confessing becomes personally attractive: 0 years instead of 1.

The situation has two distinct properties:

• Stable outcome: both confess, because neither benefits by changing alone.
• Better shared outcome: both remain silent, because both would be better off there.

The same logic appears in less dramatic settings: competing firms overspending on advertising, neighbors avoiding the cost of collective maintenance, team members withholding effort on a shared task, or organizations failing to share useful information. The labels and stakes change, but the strategic pattern can remain.

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A real-world version: pest control

The Prisoners’ Dilemma is not fundamentally about prisoners. It is about individually attractive choices creating a collectively inferior pattern.

CORE Econ’s pest-control example makes this tangible. Two neighboring farmers can use integrated pest control, which is better for their shared water supply, or a cheap chemical that works well for one farmer but creates contamination when both use it.

The farmers’ choices are stable because each farmer evaluates the other’s action as fixed:

• If the neighbor uses IPC, using the chemical is individually cheaper and more rewarding.
• If the neighbor uses the chemical, using IPC becomes ineffective because the chemical destroys the beneficial insects.

So both choose the chemical. Neither gains by changing alone. But both would receive a higher payoff if both used IPC.

This is not a contradiction. The word best is referring to two different standards:

• Best response: best for one person given the other’s current action.
• Best joint outcome: best for the group if they could coordinate their choices.

Game theory becomes useful when you refuse to blur these two standards.

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“Stable” is not the same as “inevitable” or “good”

A Nash equilibrium is often a plausible prediction, but it is not a prophecy about human behavior. Real people may cooperate because of trust, values, habits, relationships, professional norms, or a shared long-term interest. They may also talk, make commitments, change the rules, or discover information that changes the game entirely.

Equilibrium analysis says:

Within these incentives, choices, and assumptions, this outcome cannot be improved by one person changing alone.

It does not say:

This is what must happen, this is fair, or nothing can be done.

This distinction matters in workplace situations. Suppose two teams each maintain separate reporting pipelines because moving first to a shared system requires effort and carries migration risk. Continuing separately may be stable: neither team wants to absorb the migration cost alone. Still, both may suffer from duplicated work, inconsistent metrics, and slower decisions.

The practical question is not merely, “Who should try harder?” It is:

• What would make a coordinated change safe enough for both sides?
• Can the migration cost be shared?
• Can leadership set a common standard or provide temporary support?
• Can the teams make commitments that reduce the risk of being the only side to contribute?

Those questions begin to alter the incentives. In other words, they may create a different game with a better stable outcome.

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A quick field note for everyday analysis

For the next recurring interaction you notice, write a short note. Choose something low stakes: sharing a household chore, joining a meeting on time, contributing to a shared document, or coordinating plans with friends.

Use this template:

1. Outcome to inspect: What combination of choices currently seems to persist?
2. Solo-change test: If one person changed while everyone else stayed the same, would that person be better off?
3. Stability judgment: Is each person already making a best response?
4. Quality judgment: Is there another outcome that all participants would prefer?
5. Design question: What communication, norm, commitment, shared resource, or change of rules might make the better outcome stable?

Keep the final question open. At this stage, the goal is diagnosis, not forcing an immediate solution.

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Key takeaways

A stable outcome, or Nash equilibrium, is one where no participant benefits from changing their own action alone, assuming everyone else’s action stays fixed.

To identify one:

1. Hold the other participant’s choice fixed.
2. Find each person’s best response under that condition.
3. Locate an outcome where all chosen actions are best responses simultaneously.
4. Then separately ask whether another outcome would make all participants better off.

Stability is not the same as desirability. A group can be stuck in an outcome that no individual wants to leave alone even though everyone would prefer a coordinated change. The Prisoners’ Dilemma is the classic example of this trap.

Next, you will play through a Prisoners’ Dilemma mini-game and diagnose exactly why cooperation breaks down, rather than treating “lack of trust” as a complete explanation.