The question doesn’t just tap into the debate between nationalists and multilateralists that polarizes many Western countries. It’s also a timeless ethical conundrum. In a famous dialogue by Plato, an Athenian macho named Callicles argues that justice is merely the law of nature — meaning, of the strong. In our pandemic context: Why wouldn’t politicians in rich countries buy up the vaccines and give herd immunity to their own electorates first?

Socrates, in that conversation, counters that justice demands cooperation and a view that encompasses strong and weak alike. Translated for today: The world is better off sharing vaccines because survival shouldn’t depend on where you live.

But this purely moral case isn’t the only one to be made for cooperation. It turns out that multilateral sharing of vaccines would also save many additional lives.

A lab at Northeastern University in Boston has modelled two counterfactual scenarios of what would have happened if a vaccine had been available in March 2020. In one, the first two billion doses are snapped up by rich countries, while only the remaining billion are allocated among all others. In the second, all three billion are distributed from the start to all countries in proportion to their populations.

In the first or “uncooperative” case, the vaccine would have averted 33% of global deaths through September 1. In the second or “cooperative” scenario, it would have prevented 61%. That’s a lot of lives saved — even in countries that would have had the vaccine in either scenario.

The situation is therefore a bit like the famous Prisoner’s Dilemma in game theory. If all countries cooperate, the world can achieve an optimal outcome and defeat the pandemic soon and decisively. If they don’t cooperate, Covid will drag on and there’ll be many more deaths. The dilemma is that each individual country also has an incentive to “cheat", relying on others to do the sharing while snatching all the doses it can. But this leaves the others even worse off than if no one cooperated.

In game theory, the various outcomes can be tweaked by changing the mathematical parameters. And this — at least in my interpretation — is what the Eurasia Group, a geopolitical risk consultancy, is now trying to do with a new report commissioned by the Bill & Melinda Gates Foundation. The nonprofit is a lead sponsor of the ACT-Accelerator, a collaborative effort between governments, companies, scientists, and philanthropists, to get tests, treatments and of course vaccines to developing countries.

The idea is that rich donor countries pitch into a pot that funds distribution in poorer nations. But donor nations have so far ponied up only $€4.2bn. An additional €23.2 billion is needed to deliver the shots and other tools as they become available. How can we get all prisoners in this dilemma to cooperate?

By showing them that any money paid in will earn them a huge return with no downside, Eurasia Group’s report implies. The group has analyzed the geopolitical and economic costs to rich countries if the pandemic were to rage on in poor ones. These include the obvious — the impact on the Japanese economy of the Summer Olympics being cancelled, say — and the oblique, such as the effects on international demand for German exports or US fracking gas.

Overall, Eurasia Group found that the economic benefit of controlling the pandemic everywhere would be €126 billion next year for the ten top donor nations, or €384 billion over the next five years. That’s more than ten times the amount ACT-Accelerator asks for. Moreover, if you compare the ACT-A pot to the gargantuan domestic stimulus programs rich countries have passed, it starts looking almost trivial.

Rich countries have a lot of big decisions to make in the coming weeks — whether and how fast to approve which vaccine, how to allocate scarce shots in the domestic population, how to fight disinformation by anti-vaxx conspiracy theorists, and so forth. These fights may get nasty.

But the decision about whether to include poor countries in our common human struggle against a pandemic shouldn’t be so hard. If there’s any good argument for not fully and immediately funding the ACT-Accelerator, I have yet to see it.

• Andreas Kluth is a columnist for Bloomberg Opinion. He was previously editor in chief of Handelsblatt Global and a writer for the Economist.