Math Trek

By Julie Rehmeyer

Web edition: November 13, 2012

Climate treaty negotiators might be wise to have a conversation with a game theorist.

So far, negotiators’ promises to reduce greenhouse gas production have been paltry and results paltrier, as both emissions and global temperatures have risen. A new game theoretic analysis published in the Oct. 23 Proceedings of the National Academy of Sciences both pinpoints why negotiations have accomplished so little and suggests how the parties might achieve better results.

Since 2009, climate treaty negotiations have focused on one value: 2 degrees Celsius. If the planet warms more than this, scientists have warned, catastrophic changes may result. So negotiators have agreed to the goal of staying under this threshold.

Some countries have pledged greenhouse gas emissions reductions of varying amounts by 2020, but the sum of all these pledges falls woefully short of what’s been projected as needed to meet this goal.

Scott Barrett and Astrid Dannenberg, both of Columbia University, wondered whether negotiators were wise to focus on a threshold like 2 degrees Celsius. So the researchers designed a game to analyze and experimentally test how a threshold affects negotiators’ behavior.

The scientists gave members of a 10-member group their country’s “treasure”: a 20-euro national savings account, plus a fund for spending on emissions reductions that consisted of 10 black chips worth 10 cents apiece and 10 red chips worth one euro apiece. Each person could then contribute any number of these chips to a common pool. The contributed chips represented greenhouse gas reduction strategies that were relatively inexpensive (black) or expensive (red). Players could communicate freely about their plans for how many chips they intended to contribute.

At the end, the participants cashed out their remaining chips and kept the proceeds, and each also received an extra payoff of five cents for every chip in the common pool. But if the pool didn’t contain at least 150 chips, catastrophe resulted: Each player lost 15 euros from the national savings account. (Only in game theory is the loss of 15 euros equivalent to the destabilization of the world’s climate.)

So imagine yourself in the game, and suppose that everyone else says that they’re contributing nothing to the common pool. Meeting the 150-chip threshold is hopeless then, so you’re best off contributing nothing yourself. At least the full value of your unspent chips will help offset the 15-euro penalty.

But now suppose everyone else promises to contribute 15 chips. Then you’ll be highly motivated to follow suit, because then the threshold will be met and you’ll avoid the 15-euro penalty.

Theoretical analysis showed that these two strategies were the only ones in which no one would want to change their own contribution if they knew exactly how much everyone else was contributing (such strategies are called “Nash equilibria”).

When the scientists tested the game out on real people, they found that the groups almost always managed to cooperate and meet the threshold. Hooray! Catastrophe averted, planet saved!

But then Barrett and Dannenberg changed the game to make it more like the real world. Scientists can’t certify that the climate will be destabilized the moment the world warms by more than 2 degrees. They just know that the chances are higher at that point. So the researchers made the exact location of the threshold in the game uncertain. Rather than catastrophe certainly occurring if the pool had fewer than 150 chips, the threshold was randomly chosen after the chips were in and varied between 100 and 200.

Now, Barrett and Dannenberg found, the planet was in big trouble. The problem was that players were motivated to cheat a bit. Suppose everyone else pledges 20 chips. You might easily be tempted to toss in only, say, 19 chips. Then the common pool would be 199 instead of 200, which gives only a 1-in-100 chance of catastrophe — but it ups your chances of walking away with an extra euro by 100 percent. As a result, the Nash equilibrium from the previous version in which everyone contributes 15 euros disappears, and the only strategy in which no one would change their contribution is the one in which no one contributes anything.

Tests with real people confirmed an inability to resist temptation: The players proposed that everyone pay enough to make catastrophe unlikely, but then they pledged a bit less than that. And when it came time to pony up, they contributed far less still. Every time, the planet broiled.

Unfortunately, this version of the game is much closer to the one the world is trapped in. “We’re playing an experiment with the entire planet, and we can’t be sure how it’s going to come out,” Barrett says. “It’s because of that that the negotiations are having so much difficulty.”

He argues that a more promising approach is to negotiate smaller agreements including only some countries or some greenhouse gases, and to use the threat of trade sanctions to enforce the agreements.

This column originally appeared in the October 29 edition of Science News Prime.