Public Goods and Free-Riding

students, imagine living in a town where everyone enjoys a clean park, safe streets, or a firework show 🎆. These benefits are useful to many people at once, but they are not easy for one person to “own” or control. That is where public goods come in. In this lesson, you will learn what a public good is, why people sometimes rely on others to pay for it, and how game theory helps explain why some shared benefits get underprovided.

Objectives

By the end of this lesson, students, you should be able to:

Define a public good.
Explain the free-rider problem.
Analyze strategic underprovision in a simple model.

Why shared benefits are hard to provide

Some goods are easy to divide up. If students buys a snack, only students gets that snack. But other goods are different. A city park, a national defense system, or a public radio signal can benefit many people at the same time 🌳. When a good has this kind of shared benefit, people may hope someone else pays for it.

This creates a collective action problem. Each person may value the good, but each person also wants to avoid paying if possible. Game theory studies exactly this kind of strategic thinking: what happens when your best choice depends on what everyone else does?

A simple example is a neighborhood streetlight. If the streetlight is installed, everyone on the street enjoys better safety. But if each household must decide whether to contribute, some households may think, “If my neighbors pay, I can enjoy the light without paying myself.” If too many people think this way, the streetlight may never be built.

What is a public good?

A public good is typically defined by two features:

Nonexcludable: it is hard or impossible to stop people from using it once it exists.
Nonrival: one person’s use does not significantly reduce another person’s use.

For example, clean air is nonexcludable because people nearby cannot easily be prevented from breathing it, and it is nonrival because one person breathing does not stop others from breathing the same air. A lighthouse is another classic example 🚨. Ships can all benefit from the same lighthouse signal at the same time.

Not every shared good is a pure public good. A crowded park may become rival if too many people use it at once. A toll road can be excludable because drivers can be charged. Game theory often studies these goods because their features affect incentives.

A key point for students: public goods are about both benefits and incentives. Even if a good is valuable to everyone, people may still underpay for it because they cannot easily prevent others from enjoying it.

The free-rider problem

The free-rider problem happens when a person benefits from a public good without paying their fair share. A free rider enjoys the good “for free” while hoping others cover the cost.

Suppose a town needs a $100$ donation from each of $10$ households to fund a community garden. If the garden is built, every household gets $120$ worth of benefit. Then each household would be happy to have the garden. But each household also thinks: “If enough others pay, I can skip my donation and still enjoy the garden.”

That temptation creates a problem:

If everyone contributes, the garden is built.
If many people try to free-ride, the garden is not built.

This is why public goods are often underprovided by private markets. The market may work well when buyers pay directly for what they receive, but with public goods, the benefit spills over to non-payers.

Real-world example

Think of a neighborhood choosing whether to fund a security camera system 📷. If the cameras reduce crime, everyone nearby benefits. But if the payment is voluntary, some households may wait for others to contribute. If too many people wait, the system may never be installed. The result is less safety than the neighborhood actually wants.

A simple game theory model of strategic underprovision

Game theory helps us formalize the problem. Let’s build a very simple model.

Two people, students and another person, each choose whether to contribute $c$ dollars to a public good. If at least one person contributes, the public good is provided and each person gets benefit $b$. If nobody contributes, nobody gets the benefit.

Let’s assume the following:

The cost of contributing is $c$.
The benefit from the public good is $b$ for each person.
The public good is worthwhile overall, so $b > c$.

Now compare choices.

If the other person contributes

If students contributes too, students’s payoff is $b - c$.
If students does not contribute, students’s payoff is still $b$ because the public good is already provided.

So if the other person contributes, students prefers not to contribute, because $b > b - c$.

If the other person does not contribute

If students contributes, the good is provided, so students’s payoff is $b - c$.
If students does not contribute, no one provides the good, so students’s payoff is $0$.

So if the other person does not contribute, students prefers to contribute, because $b - c > 0$ when $b > c$.

This shows a strategic tension. students’s best action depends on what the other person does. There is no simple “always contribute” answer.

A payoff table

Here is the situation in a compact form:

| | Other contributes | Other does not contribute |

|---------------|-------------------|----------------------------|

| students contributes | $b-c$ | $b-c$ |

| students does not contribute | $b$ | $0$ |

From this table, you can see the free-rider incentive clearly. If the public good is already being provided, students saves the cost by staying out.

Nash equilibrium and underprovision

A Nash equilibrium is a set of choices where no player wants to change their decision alone.

In this simple model, if both players are rational and act only in their own self-interest, a likely outcome is that each wants the other to pay. If both expect the other to contribute, each has an incentive to free-ride. If both expect the other not to contribute, each may want to contribute, but coordination can fail.

This helps explain strategic underprovision: even when a public good is socially valuable, the private incentives may lead to too little of it being produced.

To see the social side, compare total benefit and total cost. If two people contribute, the public good costs $2c$ and gives total benefit $2b$. Society would want provision whenever $2b > 2c$, or simply $b > c$. But privately, each person tries to avoid paying. That gap between social benefit and private incentive is the heart of the problem.

Why governments and groups step in

Because public goods are hard to fund voluntarily, governments, charities, and community organizations often step in. Taxes can spread the cost of public goods across many people. This makes sense because the benefit is also shared across many people.

Examples include:

National defense 🛡️
Street lighting
Flood control systems
Public health campaigns
Basic scientific research

These are often funded collectively because relying only on voluntary donations would lead to too much free-riding.

There are also ways to reduce free-riding without full government control:

Making contributions mandatory
Offering matching donations
Creating clubs or memberships with exclusive benefits
Using social pressure or public recognition

For example, a school fundraiser may post a list of donors. Even if the good is public in spirit, recognition can make people more willing to give.

Connecting the model to real life

students, the simple model is not just a classroom exercise. It helps explain many real situations where people benefit from shared action but hesitate to pay for it.

Consider climate protection 🌍. Everyone benefits from cleaner air and a stable climate, but each person or country may prefer others to cut emissions first. That is a global free-rider problem. Or consider a neighborhood cleanup. Everyone enjoys the improved appearance, but each resident may prefer someone else to bring the trash bags and spend the time.

Game theory shows that the issue is not only selfishness. It is also about incentives created by shared benefits. A person can fully understand that a public good is valuable and still have a reason to hold back if others are expected to pay.

Conclusion

Public goods create one of the most important collective action problems in game theory. Because they are nonexcludable and nonrival, people can benefit even if they do not pay. That creates the free-rider problem: individuals hope others will contribute while they enjoy the result. In a simple strategic model, this leads to underprovision, because the private payoff from paying is often lower than the social value of the good. Understanding this helps explain why communities, firms, and governments use collective funding, rules, and incentives to make shared benefits possible.

Study Notes

A public good is typically nonexcludable and nonrival.
Nonexcludable means people cannot easily be kept from using the good.
Nonrival means one person’s use does not significantly reduce another person’s use.
The free-rider problem happens when people benefit without paying.
Free-riding makes voluntary funding of public goods difficult.
In a simple model, if the public good costs $c$ and gives benefit $b$, people may still avoid paying because they hope others will contribute.
A person often prefers not to pay if the public good is already being provided, since they can get benefit $b$ without paying cost $c$.
This creates strategic underprovision: the public good is provided less than is socially desirable.
Governments and other organizations often solve this by using taxes, rules, subsidies, or collective action.
Real-world examples include streetlights, clean air, national defense, public health, and scientific research.