Prisoners'-Dilemmas and Public-Goods Games

Two Global Dilemmas. Climate change and energy security are both prisoners'-dilemma (PD) games. A country that reduces emissions bears the full cost of the reduction, but gains only a tiny part of the climate benefit. A country that reduces oil consumption bears the full cost of the reduction, but gains only a small part of the savings from lower oil prices. [Technically, multi-player PD games are public-goods (PG) games.]

Cheating is Dominant. A dominant strategy pays off more than any other strategy no matter what the other players do.

  • If all other countries cooperate and reduce emissions (or oil use), it pays to enjoy a free ride on the benefits of their efforts. Cheating pays most.
  • If all other countries cheat, it would be foolish to waste money trying to solve the global problem alone. Cheating pays most (loses least).
In a prisoner's-dilemma (or PD) game, all players have a dominant strategy: do not cooperate.

The Naïve Approach. Such games have been studied intensively for 50 years, both in the real world and in experiments. And much has been learned about what can make people cooperate and when they will cheat. So what does game theory says about Al Gore's (Wash.Post) claimed solution: "If the United States leads, China will follow"?

First notice that if the U.S. leads it will make action by others less urgent but no less costly. This is "solving" the free-rider problem by guaranteeing a free ride. But perhaps he's hoping for a psychological affect.

Magical Thinking. Although Gore seems oblivious to game theory, Shafir and Tversky, two Princeton game theorists have studied the nature of leader-follower strategy with fascinating results.

Reality. In reality, achieving cooperation in a prisoners' dilemma game is possible, but not with Gore's leader-follower strategy. Unfortunately it is more difficult in games with many players, and it is more difficult when the players are groups (countries) instead of individuals. In one experiment a class of 27 students would earn $1.08 each if they all cooperated and $0.50 each if they all defected.

The students played the game a few times for practice and then they had a discussion in which one student lead a "conspiracy" to cooperate and maximize their combined winning from the professor. But 23 of the 27 students defected, so most gained only 8 cents from the "conspiracy" and the four cooperators lost everything. The leader of the conspiracy concluded "I'll never trust anyone again as long as I live." When asked how he played, he replied, "Oh, I defected."

The Tragedy of the Commons. Global warming is one example of the "tragedy of the commons," the fate that often befalls a common resource. The atmosphere/climate is such a common resource. Other "tragedy" situations are fish populations and rivers. Elinor Ostrom (2009 Nobel) has studied real-world solutions to the problem and found there are many different solutions, and what works best depends on the nature of the resource. For example, "a fisherman's catch is often difficult to monitor ... therefore rules based on quantity quotas are rarely used" (Dixit & Nalebluff).

Are Countries Like Coal Plants? The justification for cap-and-trade runs as follows. It worked for acid rain by capping sulfur (SO2) emitting coal plants. Countries emit CO2 like coal plants emit SO2, so we should put a CO2 emissions cap on countries. If you only consider emissions and environmental damage, this is a good analogy.

But the climate-policy game is different from the acid-rain game. For starters, coal plants are subject to the U.S. government, while countries are subject to no government at all. This is why Canada's strategy is to ignore its cap -- the consequences are nil. There are many other differences but the point is:

  • Once global climate policy is seen to be a game, countries no longer look like coal plants.