A firefighter douses flames from a backfire in San Andreas, California Getty Images / JOSH EDELSON / Stringer

It’s going to get a lot worse before it gets any better. According to new research published in Nature, humanity will witness marked sea level rises and frequent killer heatwaves before governments take decisive action against climate change. And to predict the future, mathematicians have turned to game theory.

The paper, published by a team of mathematicians, uses game theory to explain why it is so hard to protect the environment, updating it so they could model the effects of climate change, overuse of precious resources and pollution of pristine environments.


The bad news is that the model suggests that, when it comes to climate change, things might have to get demonstrably worse before they can get better. The good news, on the other hand, is that game theory could help policymakers to craft new and better incentives to help nations cooperate in international agreements.

The researchers used one of the best known social dilemmas in game theory — called the tragedy of the commons — to reach their predictions. The tragedy of the commons was first described in the 19th century by William Forster Lloyd, an Oxford University political philosopher. Lloyd analysed the overuse of common land (also known as a "common") by people who had rights to use it — to graze their sheep, for example — to air the idea that resources that do not clearly belong to an individual or a group are likely to be overexploited, since conserving them isn’t in the interest of the individual.

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The idea was later made famous by American ecologist Garrett Hardin, in a 1968 paper published in the journal Science. The tragedy of the commons has become one of the most used metaphors among experts to illustrate our chronic inability to sustain a resource that everybody is free to use and, alas, just as free to abuse.

We see examples of this dilemma in our daily lives, from litter on the subway to the reluctance to empty the dishwasher in the shared student kitchen. The most extreme example, however, is the current environmental crisis.


Previous attempts to come up with a mathematical model of the environmental tragedy made the unrealistic assumption that the commons remained unchanged as people exploited them – they played the same game in every round of the model. These approaches could not study the effects of a degrading environment, such as an increasingly overfished sea or a river as it was being polluted, for example. In their new Nature paper Martin Nowak of Harvard University, working with Christian Hilbe and Krishnendu Chatterjee of the Institute of Science and Technology Austria, and Stepan Simsa of Charles University in Prague, detail a more faithful way to model – and understand - the dilemma with mathematics.

“It is based on the simple idea that our actions today change the game we can play tomorrow,” Nowak says. The games in question involve encounters between people where they can either work together and cooperate or pursue their own selfish motives instead. “Depending on what you and I are doing, we move to another game so, as an example, you and I write an article together and, if we do well, we may do a book and, if this continues, we might set up a research institute.”

When they explored the new mathematical model, the scientists found that this dependence on players’ actions could greatly increase the chance that players cooperate, provided the right conditions were in place. “We have shown how environmental feedback can spur cooperation,” says Nowak, who has spent decades exploring the laws of cooperation.

These feedback factors include how quickly our resources — be it the ocean or the planet’s ozone layer — degrade. This might explain why relatively rapid action to ban chemicals such as chlorofluorocarbons were prompted when a dramatic drop in atmospheric ozone that protects life from the Sun's harmful UV rays was detected by a British team working in Antarctica in 1985. A global agreement to protect the stratospheric ozone layer, the Montreal Protocol, was finalised in 1987 and went into force a couple of years later.

This is not the case with climate change. Although we know that glaciers are shrinking, sea levels are rising, and extreme weather events — from hurricanes to heatwaves — are becoming more intense, these effects are often complex and occur over longer timescales, so establishing a clear link between them and climate change is less straightforward. This, according to Nowak, might explain why it has been more difficult to come up with effective international cooperation to curb climate change driven by greenhouse gases.


The new mathematical model suggests the global environment has to deteriorate in a dramatic way – hurricanes becoming more intense, more droughts and heatwaves – before our eyes before governments will be spurred on to make things better. “When human activity leads to drastic environmental deterioration, through global warming, cooperation becomes the winning strategy,” Nowak says.

However, this new mathematical model also enables policymakers to explore future possibilities raised by climate models and explore next steps on a more rational basis. “This opens up many new possibilities,” says Nowak. Because key impacts of climate change occur over a long timescale, one option is not to rely on environmental decline to spur policymakers into action. Instead we need to devise incentives that work over much shorter timescales, say a year or so. “We even show which feedback is needed,” Nowak says.

“You could give people, cities or countries financial incentives to work together on a problem and, if they succeed, they get these incentives and can move to bigger and more complex problems, along with even larger rewards.” The financial incentives hinge on the actions of the players, whether they are people or countries. “Cooperation leads to more valuable games, defection to less valuable ones, and can be designed to occur quickly enough to make a difference,” Nowak says. “This new approach is a game changer.”