Game Theory and the Kyoto Protocol

I thought I'd take a break from depressing news about the financial markets and tackle depressing news about the environment. I just read an article in the Economics Focus section of The Economist: Playing games with the planet, Sep 27, 2007. In that article, The Economist discusses research that analyzes the current impasse over the Kyoto Protocol from the perspective of Game Theory.

Basically, the Kyoto Protocol resembles the Prisoner's Dilemma -- a game where players should cooperate from the perspective of globally optimal payoffs, but the players have incentives that would cause them to defect from cooperation and lead to mutually harmful payoffs. The Prisoner's Dilemma can be ameliorated by converting it from its static form to a repeated game. In the repeated Prisoner's Dilemma, players can see what the other players did during previous rounds and 'punish' them for defection.

As Robert Axelrod (an American political scientist -- who took the science part seriously) and others have demonstrated, the best strategy that emerges for repeated PDs is the so-called 'tit-for-tat' strategy. In most cases, that strategy recommends that (a) players should start by cooperating, (b) if some subset of players defect, then they should be punished by the cooperating players but that this punishment should last no more than the time or magnitude required to get players back in line, and (c) hopefully, all players will return to cooperation.

Michael Liebreich, of New Energy Finance, argues that -- while the current impasse over Kyoto seems to be more like the static PD -- the situation should be seen as being more like the repeated PD. Mr. Liebreich offers hope that, with some alterations to the Kyoto and post-Kyoto attempts to control global warming, something akin to 'tit-for-tat' can bring about a global regulatory mechanism to combat global warming.

Although I admire Mr. Liebreich's no doubt good intentions, I think he is being too optimistic. The flaw with his thinking is that there is another framework to consider beyond Game Theory: externalities. As The Economist cheekily points out:

At any given summit on climate change, it is never long before some politician declares how “urgent” or “vital” or “imperative” it is to stop the planet from overheating. And yet few governments are willing to tackle the problem by themselves. In practice, what these impassioned speakers usually mean is that it is urgent—no, vital!—no, imperative!—for all countries but their own to get to grips with climate change.

This quote nicely sums up the problem with economic externalities (aka, external costs and benefits): The benefits of controlling global warming would be shared with countries not cooperating, but the costs will be borne only by those who cooperate. In other words, countries like the U.S. that refuse to cooperate with global warming treaties will free-ride off the countries that are doing something about global warming.

The logic of repeated PD and 'tit-for-tat' rests on the fact that, in those idealized scenarios, players can monitor defection and can adequately punish defectors. But with externalities, it would be difficult to monitor who benefits even though they are free-riding, and it would be even more difficult to punish free-riders without causing serious lasting damage to both the cooperators and defectors.

For example, let's say Denmark decides to punish America for not cooperating on Kyoto or Kyoto-like global warming control schemes. How would it do that? Dump toxic waste to get back at America? But that would cause lasting damage to not only America and Denmark but to the global environment itself ... precisely what they were trying to avoid!

Unlike 'tit-for-tat' of laboratory repeated Prisoner's Dilemma, in the real world global warming game, it would be hard to limit the punishment so that it would send a strong enough signal to cooperate but not so strong as to be destructive to everyone involved.

Back to the drawing board, I guess, for utilizing Game Theory for negotiating global warming treaties.