I am a scientist and a professor; I teach physics and I publish original research – mostly in physics-related publications. My degrees are actually in chemistry but I have changed my focus over time. I use mathematics often, both in my teaching and in my research, so I am proficient in areas of math that relate to those endeavors, but I have never learned or used game theory. In this area I am as amateurish as most of you. That said, this blog is dedicated to game theory. Some, especially economists, advocate using game theory to analyze optimal strategies for mitigating climate change.
A few years ago, I made contact with a mathematician – an expert in game theory, to try to explore applications of game theory in a game-simulation that I am developing together with Prof. Lori Scarlatos from Stony-Brook University that I have mentioned in earlier blogs (July 31, 2012; February 18, 2013; July 2, 2013). I have treated all these efforts as interesting academic exercises with little prospect for immediate applications. That assessment started to change after reading Tracy Tullis’ seemingly unrelated New York Times article, “How Game Theory Helped Improve New York City’s High School Application Process”:
Tuesday was the deadline for eighth graders in New York City to submit applications to secure a spot at one of 426 public high schools. After months of school tours and tests, auditions and interviews, 75,000 students have entrusted their choices to a computer program that will arrange their school assignments for the coming year. The weeks of research and deliberation will be reduced to a fraction of a second of mathematical calculation: In just a couple of hours, all the sorting for the Class of 2019 will be finished.
To middle-school students and their parents, the high-school admissions process is a grueling and universally loathed rite of passage. But as awful as it can be, it used to be much worse. In the late 1990s, for instance, tens of thousands of children were shunted off to schools that had nothing going for them, it seemed, beyond empty desks. The process was so byzantine it appeared nothing short of a Nobel Prize-worthy algorithm could fix it.
Which is essentially what happened.
Before the redesign, the application process was a mess. Or, as an economist might say, it was an example of a congested market. Each student submitted a wish list of five schools. Some of them would be matched with one of their choices, and thousands — usually the higher-performing ones — would be matched with more than one school, giving them the luxury of choosing. Nearly half of the city’s eighth graders — many of them lower-performing students from poor families — got no match at all. That some received surplus offers while others got none illustrated the market’s fundamental inefficiency.
In 2003, New York City changed its method for matching eighth graders to high schools with a system, called a deferred acceptance algorithm, that was designed by a team of professors, including one who later won a Nobel prize in economic science. The key feature was mutuality: Students submit a list of preferred schools in order, and schools prepare an ordered list of students whom they want or who meet their standards. After rounds of computer matching, schools and students are paired so that students get their highest-ranked school that also wants them. Here, in simplified form, is how it works. In this example, each school can take three students, although it can list more, and each student can list up to three choices.
This effort describes a practical solution to a big, messy, issue in the city where I live. The school admissions process affects almost everybody here.
My thought process on the connection between deferred acceptance, game theory, and climate change relates directly to the following articles. I will explain later how I think this can help us reach a global agreement in Paris.
The first paper, “The collective-risk social dilemma and the prevention of simulated dangerous climate change,” emphasizes the difficult balance between the need for cooperation and the reluctance to participate in such a cooperative activity at one’s own expense:
Will a group of people reach a collective target through individual contributions when everyone suffers individually if the target is missed? This “collective-risk social dilemma” exists in various social scenarios, the globally most challenging one being the prevention of dangerous climate change. Reaching the collective target requires individual sacrifice, with benefits to all but no guarantee that others will also contribute. It even seems tempting to contribute less and save money to induce others to contribute more, hence the dilemma and the risk of failure.
Peter Wood wrote the second article, “Climate Change and Game Theory,” which is more of a review about the connection between the two areas:
Abstract: This survey paper examines the problem of achieving global cooperation to reduce greenhouse gas emissions. Contributions to this problem are reviewed from non-cooperative game theory, cooperative game theory, and implementation theory. Solutions to games where players have a continuous choice about how much to pollute, games where players make decisions about treaty participation, and games where players make decisions about treaty ratification, are examined. The implications of linking cooperation on climate change with cooperation on other issues, such as trade, is examined. Cooperative and non-cooperative approaches to coalition formation are investigated in order to examine the behavior of coalitions cooperating on climate change. One way to achieve cooperation is to design a game, known as a mechanism, whose equilibrium corresponds to an optimal outcome. This paper examines some mechanisms that are based on conditional commitments, and could lead to substantial cooperation.
The connection between game theory and the IPCC efforts in gathering an international support for a global agreement has also been covered in the more popular press. Here is one example from the Guardian:
German academics have used the mathematics behind the strategic behaviour of countries to propose a way though the myriad impasses
America will never sign up, but the EU will if China does, which is unlikely if Africa doesn’t. No nation wants to go it alone but Russia doesn’t want to do anything, and the poor want the rich to absorb all the costs but the rich will only agree to sign if the poor do more.
Yes, I’m talking about the great game of the UN global climate talks, which resume in a few weeks’ time in Panama – the last gathering before the big annual meeting, this year in Durban, South Africa, at the end of November.
Once the details have been worked out, the same deferred acceptance algorithm that was implemented in the NYC school admissions process could be instrumental in attempts to implement global environmental agreements. One of the key obstacles to reaching such an accord is the ever-infamous NIMBY issue. The previous operating agreement, the Kyoto Protocol, restricted its scope of emissions reductions to developed countries. At the time, the US was the leading emitter. While the Clinton administration signed the Protocol, it never submitted it for ratification by the US Senate. The main reason was the argument that since China and India were not compelled to commit to change, the US would not ratify its inclusion either.
I was visiting Australia a few years ago when carbon tax had just been implemented there and it was a very lively discussion topic. The main argument that I heard was that Australia is a small country (23 million people as of 2013), meaning that what it does or doesn’t do wouldn’t make much difference in the global context. The argument that if Australia, a rich country, does not go along with a certain plan, then large developing countries such as China and India with much higher growth rates, will follow suit, didn’t carry much weight. Shortly after, the opposition party won the election there and abolished the tax as soon as it was feasible.
Deferred acceptance might be a great solution here. In most cases, the representatives of the countries that formulate such treaties don’t have the power to authorize them directly. They do, however, have the full power to formulate a working algorithm for the process. If the whole world made an agreement but its finalization was conditional upon ratification by large emitters such as the US, US politicians would be held to a considerably higher degree of accountability than usual. The blame for failure of such a global agreement would be clear. America is a strong leader in global policy. If Australia were to vote down a similar measure, there might be fewer ramifications – the rest of the world would likely still follow the new rules.
Incorporation of a game theory technique such as deferred acceptance in the coming Paris agreement has a decent chance of preventing the instances of abstention that severely limited the Kyoto Protocol, and might increase the likelihood of success.