Human interaction and decision-making are challenging to quantify. When we think about all the factors that play into a decision or encounter between groups of people—each person’s motivations, the amount of information each person holds, the cooperation between different people involved—the system quickly becomes a vast complex of inputs and outputs, with no clear function on how to get from one to the other.
Mathematicians, undeterred by this challenge, have managed to develop some solid theory behind decisions, particularly when risk and reward are on the line. This is known as game theory, and it’s likely that some of you have seen this in your classes. Some of the seminal works in the theory are by the great mathematician John Nash, who focused on “game” models related to economics—these works have become pillars of modern mathematical finance.
I’d like to describe a particular game that was developed in game theory’s infancy. Despite its broad applications, it has a very specific name: “the prisoner’s dilemma.” As you’ve probably guessed, the problem is commonly formulated as a scenario involving two prisoners who are suspected of committing a crime. Typically, these prisoners are presumed to be part of the same criminal gang, although the police have detained them in solitary confinement, so the suspects have no way of communicating with each other.
The dilemma is that the cops offer a bargain to each of the prisoners as they go to question them. If neither prisoner talks, then they will each serve a small sentence—let’s say one year—on a lesser charge. If one prisoner provides information on the other, however, they will be set free, and the prisoner who gets ratted on will serve a larger sentence—let’s say three years. Lastly, if both prisoners snitch, they will each serve a middle sentence—let’s say two years.
Even with a relatively simple situation (there are only four possible outcomes), it’s hard to say which is the optimal strategy for each prisoner. What game theory tells us, though, is that the prisoners will inevitably choose to betray each other, snitching on the other and ending up serving two years each. It would be in their best interests to keep mum and just serve one year. But the potential disappointment of staying silent and having the other prisoner rat them out and going scot-free while they serve the longest possible sentence overrides this desire for cooperation.
This dilemma can be generalized to many real-world cases, and the one I find most fascinating deals with policy to combat climate change. Although this dilemma is now on a much broader scale, it retains the core features. The nations of the world would all benefit most by cooperating to reduce emissions and transition to clean, sustainable energy. However, even if an agreement is reached, there is no guarantee that all the governments involved will adhere to it. Rather than put in lots of effort to combat climate change while other countries continue to harm the planet, the governments of the world have mostly opted for maintaining the status quo or making emissions targets much lower than what scientists deem necessary to prevent increasing environmental turmoil in the coming decades.
What do we do about this? Game theory seems to say that there’s no way out of this result. But the climate change policy debate doesn’t have to be a prisoner’s dilemma. Governments could pledge more commitment and provide more transparency on their progress to reduce emissions. Developed nations could also provide financial support for clean energy projects around the world, not just within their borders.
The silver lining for the prisoner’s dilemma is that, if repeated, the prisoners would eventually opt to cooperate. We have done a lot of damage to Earth over the years, so cooperation on climate change may look like a damage control strategy. But fortunately, there is a way to break free of this dilemma in the long run—let’s just hope that this comes soon enough.
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