Hegemony and global public goods

Say who pays for open sea lanes and what they get for it.

A patrolled shipping lane is available to every ship that uses it, including the ones flying the flag of a country that contributed nothing to the patrol. You cannot bill them, you cannot keep them out, and their using it does not use it up. That combination has a name and a set of consequences, and the consequences explain a large share of how the world is arranged.

The good that cannot be sold

A public goodin the technical sense is one that is non-excludable, meaning you cannot keep non-payers out, and non-rival, meaning one person's use does not reduce anybody else's. Open sea lanes qualify. So do a stable reserve currency, a set of technical standards, disease surveillance, and basic research.

Everybody wants these things and nobody can be made to pay for them. The usual conclusion is that they do not get provided at all. What actually happens is more interesting.

Largestpays 25
State 2pays nothing
State 3pays nothing
State 4pays nothing
State 5pays nothing
State 6pays nothing
State 7pays nothing
State 8pays nothing
All togetherwould buy 47

What each state wants on its own. Only the tallest bar gets built, and every state below it finds its own level already met.

Sea lane patrolled

68%

If they coordinated

80%

States paying nothing

The payer still nets

18.3

The largest state buys 25 units of patrolling and seven others pay nothing. Nobody is being fooled: the payer nets 18.3 after paying for all of it, which is why it keeps paying. It is simply buying what it wanted, and there is no way to keep anybody else out.

Shrink the largest state toward the second largest40

Each bar is what one state wants on its own. Only the tallest gets built, because every state below it finds the level it wanted already there and stops. Nobody in that picture is behaving badly.

Worked example

The exploitation of the great by the small

Each state contributes up to the point where one more unit of patrolling is worth what it costs to that state alone. With a benefit v, a cost c, and coverage that saturates, the level a state wants is √(v·k ÷ c) − k, which depends only on its own benefit.

The largest beneficiary provides all of it. It wants the most, so it builds first, and there is nothing left for anybody else to want.
Seven states pay nothing, correctly. Each of them checks whether more patrolling is worth it to them, finds that it is not at the level already provided, and stops. That is the right answer for each of them individually.
The payer still comes out ahead. This is the part that makes it stable. It is not being tricked and it is not being generous. It bought something it wanted at a price it was willing to pay, and it could not stop anybody else from benefiting.
The good is under-provided anyway. What everybody together would have chosen is substantially more than what one of them chose alone, and the gap is welfare nobody captures.

Mancur Olson named this the exploitation of the great by the small in 1965, and the phrase is better than the usual reading of it. Nobody is exploiting anybody. The structure allocates the bill to whoever wants the thing most.

The logic is Mancur Olson's, in The Logic of Collective Action, 1965, and the application to alliances is Olson and Zeckhauser's 1966 paper on NATO burden sharing. Charles Kindleberger's The World in Depression made the case that the 1930s went as badly as they did partly because Britain could no longer provide these goods and America would not yet. The figures above come from the model on this page, which is unit tested.

ConventionHegemonic stability theoryis the claim that an open trading order needs somebody large enough to want it for their own sake, because the goods it depends on cannot be sold. It is contested, and the useful part is not the grand claim but the mechanism: some arrangements are only provided when one party's stake is large enough to justify paying for the whole thing. That mechanism holds whether or not the historical story built on it does.

What happens when the payer shrinks

Drag the slider and watch. The largest state's stake falls, so the level worth buying to it falls, so provision falls. And nobody replaces it.

That last part is the one people get wrong. The intuition is that if the biggest power steps back, the next few will club together. They do not, and it is not because they are short-sighted. Each of them still individually wants less than what is already being provided, even at the reduced level, so each of them still correctly contributes nothing.

The good thins out and no decision to thin it out is taken anywhere. That is a more uncomfortable account of a declining order than either the version where somebody withdraws or the version where a rival pushes them out.

What breaks

Reading the payer as altruistic. It is buying something it wants. The benefits to everybody else are a side effect it cannot prevent, and describing them as generosity makes it harder to predict what happens when the calculation changes.

Reading free riders as ungrateful. Contributing nothing is the correct decision when your desired level is already met. Moral framing here predicts nothing and structural framing predicts quite a lot, including which allies will contribute and which will not.

Assuming everything called a public good is one. Most things are partly excludable, which changes the answer completely. If access can be tied to contribution, even loosely, the free riding shrinks and provision improves. Arguing about whether something is really non-excludable is usually more productive than arguing about who ought to pay.

What to do with this

When a shared thing is being under-provided, ask two questions. Can anybody be kept out of it, and whose stake is large enough to justify paying for the whole thing? Those two answers predict the outcome better than any account of who has been reasonable.

And when you hear that allies should pay their share, notice that this is a claim about structure dressed as a claim about character. The fix is to make the benefit excludable or to replace the shared pot with specific commitments that can be checked. Neither of those is a request. They are changes to the thing that produced the behavior.

Test yourself

01A large country complains that its allies do not pay their share of a shared defense. Is the complaint correct, and does it have a fix?

The observation is correct and the framing is off. Each ally is contributing the amount that is worth it to them given what is already provided, which for most of them is nothing, and that is the right decision for each of them. Nobody is cheating.

The fix has to change the structure rather than appeal to fairness. Either make some of the benefit excludable, so contributions can be tied to access, or shift from a shared pot to specific commitments that can be individually verified. Asking people to pay for something they will receive anyway rarely works, and it is not because they are ungrateful.

02Why does the country paying for it keep paying, if everybody else is free riding?

Because it is still ahead. It buys the level of the good that is worth buying to itself alone, and the benefit it gets exceeds what it paid. The free riding is a side effect it cannot prevent rather than a loss it is absorbing. This is the part of the arrangement that makes it stable, and it is also why the complaining rarely turns into withdrawal.

03The hegemon's share of the world economy halves over thirty years. What happens to the public good, and who decides it?

It degrades, and nobody decides it. The level worth buying to the largest beneficiary falls with its stake, so it provides less. No coalition of the others replaces it, because each of them still individually wants less than what is already there, even at the reduced level.

That is the uncomfortable version of the argument about a declining hegemon. The good does not end because anybody withdrew or because a rival pushed it out. It thins out because the arithmetic that produced it in the first place is producing a smaller number.

A tutor that knows this lesson. It asks before it explains, and it will not tell you what to do with your own money.

Educational material, not investment or policy advice. Figures are cited where they come from a filing or a statistical series, and labelled as illustrative where they do not.