23. Collective Action Problems
Managing environmental resources sustainably has always been difficult,
ever since Homo sapiens developed modern inventiveness, efficiency, and
hunting skills by around 50,000 years ago.
—Jared Diamond
In this chapter, we cover collective action problems: situations in which
self-interest does not align with the collective interest. These problems arise
in matters small and large. At airports, travelers individually benefit by
standing as near as possible to the baggage carousel, but collectively
everyone would be better off if people stood back a few feet. In a
democracy, people have little incentive to become informed voters given
the very low probability of a single vote turning an election, yet a
democracy performs better with an informed citizenry. Collective action
problems can be thought of as many-player Prisoners’ Dilemmas: each
person has an incentive to defect, but collectively, everyone does better by
cooperating.
People often study collective action models in the context of historical
examples such as the management of the Scottish commons or the lobster
habitats along the coasts of Newfoundland and Maine.1 History also
contains dramatic failures. Among the most famous is the collapse of the
Polynesians on Easter Island, described by Jared Diamond.2 Easter Island
lies over two thousand miles west of Chile in the South Pacific, with no
other inhabitable island within a thousand miles in any direction. Given that
location, Easter Islanders have always had to manage for themselves. For
over a thousand years they lived well. Some estimate that by the early
seventeenth century, Easter Island’s population exceeded fifteen thousand

people. In the sixteenth century, the Easter Islanders marshaled sufficient
resources to free up labor to build giant stone heads, called maoi, that weigh
up to eighty tons. While the Easter Islanders were busy constructing maoi,
they were not cooperating in the management of their forests. By 1722,
when Europeans first landed on the island, food was relatively scarce and
the population had dropped to around two thousand. Few trees over ten feet
tall remained. Many species of birds and animals had gone extinct. To use
Diamond’s phrasing, the civilization collapsed. The collapse became
complete when viruses carried by the Europeans killed nearly all of the
remaining population.
According to Diamond’s account, the collapse of the civilization on
Easter Island, as well as the collapses of the Mayans in Central America,
the Anasazi in the American Southwest, and the Vinlanders on Greenland,
resulted from a combination of overharvesting of natural resources (caused
by institutional and cultural failures) and climatic changes. The Vinlanders
grazed animals on marginal land and tore up fragile sod to make houses. In
short order, the land became barren from overuse, and the Vinlanders
starved. Like the Easter Islanders, the Vinlanders had failed to manage a
common pool resource. By chopping down too many trees and using up too
much turf, they produced a collapse.
Though evocative and compelling, these examples lead many to see
collective action problems as something of relevance only in the past. That
framing is unfortunate. As the world becomes more interconnected and
complex, collective action problems are far more relevant today. We
confront collective action problems at almost every scale of human
organization. The provision of public education, physical and mental health
care, infrastructure, public safety, a justice system, and national defense are
all collective action problems, as are managing global fisheries, combating
climate change, and in particular reducing the amount of carbon in the
atmosphere. In addition, as work becomes more team-based, it necessarily
produces collective action problems. Workers have incentives to free ride
on the work of others. They also have incentives to overdemand shared
workspaces to ensure space for their teams to work.
The chapter is organized as follows: We first define a generic collective
action problem, and then analyze three specific types. We start with public
goods provision problems, in which individuals contribute money to fund

roads, schools, and social services or time and effort to clean a park or
watershed. We then study congestion problems, where individuals must
restrict use of a resource such as a road system, beach, or park. We finish
with renewable resource extraction problems, where individuals consume a
resource that can regrow, such as fish, lobster, and trees. Congestion
problems reset each day. If too many cars clog London’s streets, the city can
increase the fee on cars entering the city and solve the problem, and so past
overuse has no long-term effects. However, an overharvested forest or
fishery takes decades to regrow. We pay consequences for past failures to
cooperate.
In each of the three specific models, the nature of the misalignment
between individual incentives and collective goals differs, so solutions
differ as well. We can solve public goods problems through taxes, and in
some cases through sorting. Congestion problems can be solved with fees
or usage restrictions. Solving renewable resource problems requires more
elaborate monitoring and sanctions as well as conflict resolution
mechanisms.
The solutions we offer here provide foundational insights that must be
tailored to a local context. Any real-world situation includes layers of
complexity that our models leave out. Balinese water temples solve a water
allocation problem that is a sequential congestion problem, with upriver
people drawing the resource first. International fishing rights that limit
access solve a common pool resource problem with a moveable resource, as
Norway’s solution to coastal fishing could be undermined by overfishing in
the nearby waters of Sweden, Russia, and Denmark.3 Real-world solutions
rely in part on the mechanisms discussed in Chapter 22 for building
cooperation in the Prisoners’ Dilemma: repetition, reputation, network
structure, and group selection. Group selection enters indirectly:
communities and nations that succeed in solving these problems will thrive,
and their successes will be copied by others.

Collective Action Problems
In a collective action problem, each person has a choice between
contributing and free riding. Free riding is in the individual’s best interest. It
earns her a higher payoff. Yet when everyone contributes, people receive
greater benefits.

A Collective Action Problem
In a collective action problem, each of N individuals chooses to free
ride (f) or contribute (c) to a collective action. An individual’s payoff
depends on her own action and the total number of cooperators.
Individuals receive a higher payoff from free riding, Payoff(f, C) >
Payoff(c, C +1), but the sum of payoffs is maximized when everyone
contributes.

A collective action problem can be represented as a many-player version
of the Prisoners’ Dilemma. We can thus refer back to the solutions proposed
in Chapter 22 to get insights into how to create and maintain cooperation.
However, those approaches will be incomplete for two reasons: collective
action problems involve groups and communities, not just pairs, and many
collective action problems take particular forms that make solutions more
effective than others.

Public Goods
Our first specific type of collective action problem involves public good
provision. Public goods satisfy non-rivalry (one person’s use in no way
interferes with any other person’s use) and non-excludability (individuals
cannot be prevented from use). Public goods include clean air, the national
defense, early tornado warning signals, and the production of knowledge.
The United States Constitution lists establishing justice, ensuring domestic
tranquility, and providing for the common defense as responsibilities of the
government. These too are public goods.
Private goods—bicycles, oatmeal cookies, and protractors—are neither
non-rival nor non-excludable. Knowledge is both. Juxtaposing an oatmeal
cookie and knowledge of trigonometry highlights the difference. A teacher
might say, “Carla ate the last oatmeal cookie, so no one else can have one.”
She would never say, “Melissa, I am so sorry, but Carla just used the
Pythagorean theorem, and now no one else can use it.”
The non-excludability and non-rivalry of public goods produce a
collective action problem not because people do not want to contribute.
They do. The problem arises because people undervalue their contributions.
For every dollar a person contributes, she adds to everyone’s utility. In the
formal model we describe here, each person allocates her income between a
public good and a representative private good. Think of the private good as
money that can be spent on anything else. Extending the model to include
multiple public and private goods would only complicate the analysis.

A Public Good Provision Problem
N people each allocate an income I > N between a public good
(PUBLIC) and a private good (PRIVATE) that each cost $1 per unit.
Each person has the following utility function:

Socially optimal allocation: PUBLIC = N (if N = 100, each person
contributes $100).
Equilibrium allocation: PUBLIC =
contributes $0.01).4

(if N = 100, each person

In the model, we assume that utility is concave in the public good and
linear in the private good. Those two assumptions require motivation.
Recall that concavity corresponds to diminishing returns: as a person
consumes more, she values it less. Concavity in the amount of the public
good implies diminishing marginal returns to the public good. This is a
standard assumption. People benefit more from adding a third lane to the
highway than from adding a fourth lane. People benefit more from cleaning
heavily polluted air than from removing the last few particles per billion.
We assume linearity in the private good because it represents a composite of
all private goods. While utility may be concave in any one good, be it
chocolate, televisions, or denim jackets, it is probably closer to linear for all
goods. The assumption has the added advantage of making the model easier
to analyze.
We first solve for the socially optimal allocation, which we define as the
allocation that maximizes the sum of the utilities of the population: the
greatest happiness of the greatest number.5 The socially optimal allocation
calls for each individual to allocate $1 to the public good for each member
of the population. Notice that the amount each person contributes to the
public good increases with population size. This result does not depend on

our particular function. It follows from the fact in a larger population, the
non-rival public good can be enjoyed by more people. More people enjoy
clean air or national defense, so more should be provided.
The equilibrium contributions equal 1 divided by the population size. As
the population increases, people have a greater incentive to free ride off the
contributions of others. We can see why by increasing the population size
by one. This new person receives the same utility from the public good as
everyone else had previously. If other people’s contributions stayed the
same, this new person has weaker incentives to contribute to the public
good than the others had previously. Therefore, he will contribute less than
the others contributed. Moreover, whatever amount he does contribute
increases the total amount of the public good and creates an incentive for
everyone else to contribute less than they had previously.
The model thus reveals that as populations become larger, public good
provision problems exacerbate. The optimal level of the good increases,
while the incentives to give fall. The formulae for amounts derived in our
model (the N and ) do depend on the functions assumed, but the
phenomenon of underprovision holds more generally.
This analysis assumes self-interested people, a common assumption in
economic models. Evidence from surveys, experiments, as well as casual
observations, reveals that people often have other-regarding preferences.
People want good schools and roads for others as well as for themselves.
We can include other regarding preferences by adding an altruism
parameter to our model. A value of zero for that parameter corresponds to
the self-interested rational actor from economics, and a value of 1
corresponds to everyone caring as much about others as they care about
themselves. As shown in the box, pure altruists, people who care about
everyone equally, contribute the socially optimal level. Anything less than
pure altruism leads to underprovision.
The calculations show that in large populations, people contribute a
portion of the optimal level that is (approximately) equal to the square of
the altruism parameter. Though the extent of underprovision depends on the
utility function, the example demonstrates the limits of altruism. People
who care about others half as much as themselves contribute one-fourth of
the optimal level. People who care about others a third as much as

themselves contribute a mere one-ninth of the optimal level.

Public Good Provision Among Altruists
N people have altruistic preferences with weight α on aggregate
utility:

Equilibrium pure altruists (α = 1): PUBLIC = N
Equilibrium general solution:6 PUBLIC =
Example: α = : PUBLIC ≈

Given that we do not live in a world of pure altruists, we must look to
other mechanisms, such as taxation. Governments impose taxes to pay for
roads, national defense, education, criminal justice systems, and other
public goods. Determining the amount of the tax requires a more elaborate
model that includes income and preference heterogeneity. People could vote
on an amount and a common tax rate. The spatial voting model predicts a
tax rate equal to the preferred level of the public good for the median voter.
That level may not be socially optimal if people have heterogeneous
incomes and preferences.
Many public goods such as schools, roads, and recycling programs can
be classified as local. A local community can exclude others, but within the
community the public good is non-rival and non-excludable. For local
public goods, allowing people to sort into communities based on their
preferences, what is called Tiebout sorting, offers a possible solution to the
public good provision problem. People who want better schools, public
parks, pools, and police protection can vote for higher taxes to pay for those
public goods. Those people who do not want the local public goods can live
in a separate community and pay lower taxes. Tiebout sorting is not a cureall. It brings attendant costs, including lower social cohesion. Moreover,

when high-income people isolate themselves, they reduce public good
provision in poorer communities and reduce network interactions that can
transfer information and knowledge.7

The Congestion Model
In a second type of collective action model, involving resources such as
roadways, beaches, and water systems, the value to an individual decreases
with the number of users. Anyone who has spent time stuck in traffic has
experienced a congestion problem. A wide-open road brings more pleasure
and utility than one clogged with cars. Estimates place the costs of traffic
delays in the United States in the neighborhood of $100 billion a year. In
some cities, notably Los Angeles and Washington, DC, commuters spend,
on average, more than sixty hours per year in traffic.
Our congestion model assumes a resource of fixed capacity. Each day,
people can use the resource or abstain. An individual’s benefit from using
the resource decreases linearly with the number of other users.8 The slope
of the line, the congestion parameter, captures the magnitude of the
congestion effect.

A Congestion Model
M of N people choose to use a resource. Their utility can be written as
follows:

Utility(M) = B − θ · M
where B denotes the maximal benefit, and θ is a congestion parameter.
The remaining (N − M) people abstain and receive utility of zero.9
Socially optimal: M =

Utility

=

Nash equilibrium: M = Utility( ) = 0

In the socially optimal solution, the number of people who use the
resource equals the maximal possible benefit divided by twice the
congestion parameter. Those findings align with our intuition. The number
of people who use the resource should increase with the maximal benefit
and decrease with greater congestion effects. In the Nash equilibrium
solution, exactly double the socially optimal number of people use the
resource. Congestion becomes so severe that no one receives any benefit.
That result is an artifact of the assumption that not using the resource gives
a utility of zero. This finding has the counterintuitive implication that a
community that builds a beautiful park may not produce much utility for its
citizens. In equilibrium, the park will be sufficiently crowded such that
being at the park is no more enjoyable than staying home.
When a model produces a result that runs counter to common sense, we
need to reason through the result. People must be happier having a park, so
the model must be wrong. It is wrong, because we assumed identical
preferences. If people vary in how much they enjoy the park, then some
people may be receiving positive utility, while others get no benefit.
Second, the model assumes the park is always crowded. That will not be

true. Third, the alternative option might be going to the beach, not staying
home. The new park may make the beach less crowded. Finally, people
enjoy diverse experiences. If the city has a skateboard park, a dog park, and
a water park, then people may get benefits from the diversity of experience
over a period of weeks.
Those challenges notwithstanding, the main result still has some teeth.
During busy times, congestion will rise to the point where the park
produces no more benefit than any other activity. Crowding will still occur,
though not as much as when there was a single park. In addition, as shown
in the box below, the creation of multiple parks offers no guarantee that
people allocate themselves across those parks optimally. In the example
shown in the box on the next page, in equilibrium, too many people go to
the larger park.
In addition to creating more parks, a community could try other
solutions such as rationing, rotating access, running a lottery, fees, and
enlarging capacity. Rationing gives each person or household a fixed
amount of the resource. This solution works for divisible resources like
water. It is less practical for roads. Rotation schemes divide use of the
resource by time. During air pollution alerts, a city can restrict roads to cars
with even- (or odd-) numbered license plates on certain days. Other
resources, such as placements in popular public schools, cannot be rationed
or rotated. In those cases, lotteries can be held.

Multiple Congestible Goods
M people go to Park 1 and (N − M) go to Park 2. To account for Park
2 being larger, utilities are as given below:10
Park 1: Utility(M) = N − M
Park 2: Utility(N − M) = 3N − 3 · (N − M)
Socially optimal: M =

creating total utility N2

Nash equilibrium: M =

creating total utility

For access to roads, fees are a popular solution. The city of London
charges a fee to enter the central city. Limited-access toll roads around the
world do the same. Usage fees allocate the resource to those willing to pay
the most. These may not be the people who would get the most utility.
Singapore uses a combination of fees and limited access. Singapore
auctions a fixed number of motor vehicle permits each year. The permits,
which last for ten years, often sell for more than the price of a typical car.
To reduce congestion during peak times, Singapore, like London, also
charges fees for driving into the central business district. Singapore’s traffic
moves smoothly for a city its size, and the government raises substantial
amounts of money, which can then be used for public transportation.
Enlarging the capacity of roads has had mixed success. When a city adds
lanes to highways to increase traffic flow, it makes housing near the
highways more desirable, a positive feedback. A resulting increase in
housing creates more traffic, requiring even wider roads, producing a
positive feedback loop similar to those described in the systems dynamic
models covered in Chapter 18.

Renewable Resource Extraction
Last, we consider renewable resource extraction, in which individuals share
a resource that regenerates itself. This model applies to forests, watersheds,
grasslands, and fisheries. In each case, the amount of the resource available
in the future depends on how much we use now. If too much was used, the
resource may not regenerate fast enough. The need for regeneration of the
resource makes these problems more fragile than public good problems or
congestion problems. A city that underfunds public lighting in one year can
increase spending the next year without enduring long term effects from its
mistake. If a community overfishes a stream or overharvests a forest, it pays
lasting costs because to make fish, you need fish. You do not need
streetlights to make streetlights. Furthermore, the renewable resource may
be a necessity: food to eat, water to drink, and fuel to keep warm. People
need to extract the resource to live.

Renewable Resource Extraction Model
Let R(t) denote the amount of a renewable resource at the start of
period t. Let C(t) equal the total amount consumed in period t, and g
denote the growth rate of the resource. The amount of the resource in
period t + 1 is given by the following difference equation: 11

R(t + 1) = (1 + g)[R(t) − C(t)]
The equilibrium consumption level:

Renewable resource extraction problems exhibit a tipping point in the
level of consumption. Any rate of consumption above the equilibrium
extraction rate will produce a collapse, as can be shown in a formal model.
We can think of the amount of the resource as a circular field, a pie.
Consumption takes a bite out of that pie. Growth regenerates an amount of
resource proportional to the amount remaining. For low levels of
consumption, the resource will increase in size. But regrowth will not be
able to compensate for high levels of consumption. In between lies an
equilibrium level of consumption exactly balanced by regrowth.
If consumption exceeds the equilibrium level, the model predicts
accelerating declines that become steep collapses. The slow decline
followed by a steep collapse sends a warning for those who manage
resources that are difficult to measure accurately, such as fish stocks.
Annual catches give a clue, but they are not exact. We should not be
surprised that cod fishing in the North Atlantic produced a modern collapse
to rival that suffered by the Vinlanders, as described by Jared Diamond in
his book on collapsing societies. Cod had been fished in the North Atlantic
for over five hundred years. British explorers who first visited the Canadian
coast told tales of catching cod in baskets and having difficulty rowing
through the prodigious shoals of cod. By 1992, Canada had imposed a
moratorium on cod fishing.12

Our model of resource extraction assumes a constant growth rate,
allowing us to solve for the equilibrium consumption level. In reality,
growth rates vary from year to year. In the case of a pasture, growth
depends on temperature and rainfall. For a fish population, the growth rate
depends on the amount of available food, which in turn depends on
variations in weather or on climatic changes.
In the other two models, variation would not have long-term
consequences. Some years we might have too much of a public good or a
little less congestion. Those would affect utility, but perhaps no more than
the inevitable variation in the weather. But in renewable resource extraction
problems, variation leads to either collapse or abundance, provided that
behavior does not change. Figure 23.1 assumes an average regeneration rate
of 25% and 100 units of a resource. Given those assumptions, the
equilibrium consumption level equals 20 units per year. The figure assumes
a variable growth rate randomly drawn between 20% and 30%. The model
also builds in a maximal level of the resource set to 150.

Figure 23.1: Ten Possible Paths Assuming Variation in Growth Rate of Resource

In approximately half of the paths, the level of the resource collapses. In
the other half, the level of the resource increases to the maximum possible
level. The variation does not cancel out. To the contrary, the effect of a
reduction or increase in growth accumulates over time.13 From this
simulation, we see that optimal consumption policy would call for less
consumption following lean years to prevent collapse.
Given that variation in the growth rates of a renewable resource requires
consumption to vary with the resource level, we know that communities
that manage a renewable resource must be able to adjust extraction levels.

The method or mechanism used to make those adjustments depends on
features of the resource. To borrow a phrase, “There are no panaceas.”14 No
single solution will work in all cases. How local populations solve these
types of problems depends on characteristics of the resource and the
community.
Fish differ from cattle. A community managing multiple herds of cattle
sharing a commons can monitor the behavior of individuals and the level of
the resource (the amount of grass). Overgrazing can be solved by rotation
schemes that allocate to each individual set times or zones for grazing.
These rotations can adjust grazing based on the height of the grass. But for
communities that fish, managing the resource requires more elaborate
institutions that can precisely monitor individual behavior. The number of
fish in the sea cannot be counted. It can only be estimated based on catches.
The resource extraction problem has much more uncertainty than the cattle
situation. Managing a common aquatic resource requires conservatism and
more monitoring.

Collective Action Problems: Solved and Unsolved
In collective action problems, the outcomes that result from self-interested
behavior do not align with the goals of the individuals. As noted, these
problems occur in myriad settings. They arise in paying for non-rival and
non-excludable goods. They arise in decisions for when to drive on
highways. They even arise in how we drive on highways. Drivers on a busy
highway who tailgate or talk on their cellphones may not take into account
the costs of those actions to all of the cars behind them if an accident
occurs.
Such problems exist at multiple scales. They arise within family
interactions: keeping the house clean, making dinner, going shopping, and
saving for vacations can all misalign individual incentives and collective
well-being. They exist with communities, regions, and countries in the
provision of public goods and the use and management of limited resources.
They also exist at a global scale in the form of carbon emissions. Most
countries would prefer to produce more energy themselves (which emits
more carbon) but have lower global emission levels: individually rational
actions do not align with the common good.
Collective action problems occur in the natural world as well. Trees in a
forest compete for light and water. If a tree species evolves a higher canopy
or deeper roots, it will increase its own chances of survival but impose a
cost on other species of trees. The trees cannot pass laws to prevent
growing too tall or tapping into deeper water. They do not achieve the
socially optimal solution.15
Collective action problems tend to be easier to solve the smaller and
more homogeneous the group of individuals or actors involved and the
better the information (i.e., actions are easier and the state of the system can
be monitored). While families generally solve collective action problems,
international organizations find cooperation much harder. Efforts to reduce
carbon emissions require coordination among a large group of diverse
actors using imprecise monitoring mechanisms. Solving such a problem
requires coordination as well as an enforcement mechanism. History
teaches us that overfishing waters or overgrazing meadows invites the risk

of collapse. We can apply that same reasoning to the collective action
problems we face today. Elinor Ostrom, who spent decades studying realworld efforts to solve collective action problems, found that in addition to
monitoring deviations, communities that solve collective action problems
agree on clear boundaries, agree on well defined rules, grant the authority to
impose graduated sanctions, and establish mechanisms to resolve
disputes.16