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Posts Tagged ‘Game Theory’

Economics and Global Climate Change

In popular economics, reblog on July 15, 2009 at 11:53 am

Conor Clarke, correspondent for The Atlantic, lists the reason why it’s difficult to make sense of global climate change after his interview with Thomas Schelling, who won the 2005 Nobel Prize in Economics. Schelling has been recognized in the field of game theory, which is the study of strategic situations. A strategic situation, by layman’s definition, is simply a situation where the outcome of one’s decision is affected by the decision of another party.

The rationale for the interview is to contextualize the issue of global climate change in complicated bargaining agreements among nations. Part one of the interview can be found here. He summarizes the difficulty of making sense of the issue in the following:

1. Any solution to climate change must have a theory for what the present generation owes future generations. That’s hard. How do we weigh the interests of people that don’t yet exist?

2. Any global solution to climate change must take account the fact that the costs of warming will be borne unevenly around the world. Parts of the northwestern United States will actually benefit from a warmer climate. Bangladesh will not. But why should the U.S. care what happens in South Asia?

3. Any solution should account for the fact that the responsibility for global warming is also borne unevenly. The developing world will bear most of the costs, but the developed world bears most of the responsibility. (My understanding is that this will change at some point in the next 50 years.)

4. Related to #2, the world’s ability to adapt to a changing climate is distributed unevenly. It would surprise no one to learn that wealthy nations will have an easier time adapting than poorer ones. So should we allow poorer nations to pursue the most rapid growth possible, before the consequences become dire? Or should we pursue a solution that achieves the maximum possible reduction in global emissions?

5. There is a great deal of uncertainty about what will happen. To be sure: There is no (repeat, no) scientific uncertainty as to whether or not the climate is warming. It is. But the question is, By how much? And when? Will the temperature increase by two degrees Celsius over the next 100 years? Three degrees? Seven degrees? The differences matter.

6. Climate change has an incredibly long time horizon. Any small cost or small chance of a catastrophic outcome must to weighed across hundreds or thousands of years. There is also one-way ratchet here: It isn’t clear everything we change about the climate can be reversed.

7. Global warming asks us to weigh economic factors — growth, GDP — against non-economic ones, like the diversity of species and the amount of arable land on the planet. I have absolutely no clue how to do that.

Thomas Schelling

Related post:
Game Theory of Washing Dishes

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Game Theory of Washing Dishes

In academia, popular economics on June 3, 2009 at 5:00 pm

Ben and Jack are roommates in a condo unit. Someone cooked dinner and did not wash the dishes. Each person has two possible choices: to wash the dishes or not. Let ‘Y’ be to wash the dishes and ‘N’ to do nothing.

Since each outcome will produce a pair of strategies, we will signify the pairs as (Y,Y), (Y,N), (N,Y), and (N,N). The first item in each pair is Ben’s choice, while the second item in each pair is Jack’s. The four possible outcomes are:

1. Ben will wash the dishes, Jack will do nothing (Y,N)
2. Ben will do nothing, Jack will wash the dishes (N,Y)
3. Both will wash the dishes together (Y,Y)
4. Nobody will wash the dishes (N,N)

Now we need to know which outcomes are preferred and which are not. Let’s assign a “payoff” for each outcome to signify what the roommates want and care about. The following figures are units of pleasure or utility (the higher, the happier) from the point of view of Ben:

3 if Jack will wash the dishes alone (N,Y)
2 if both will wash the dishes together (Y,Y)
1 if nobody will wash the dishes (N,N)
0 if Ben will wash the dishes alone (Y,N)

But Ben’s payoffs apply to the other roommate in reverse, so that Jack’s payoffs are:

3 if Ben will wash the dishes alone (Y,N)
Same payoffs for (Y,Y) and (N,N)
0 if Jack will wash the dishes alone (N,Y)

A roommate’s best-case scenario is to get the other to wash the dishes. The worst-case scenario is that a roommate will wash the dishes alone while the other slacks off, because we assume that resentment is costlier and more disadvantageous than having a dirty condominium where nobody washes the dishes (N,N).

Now let us set up the matrix, where each pair has the form (Ben’s payoff, Jack’s payoff).

Outcome and Payoff Matrix (please ignore the dots)

…………………Jack

………………….N       Y

Ben………. N  (1,1)  (3,0)

…………….Y  (0,3)  (2,2)
If you’re Ben, should you wash the dishes or not? Pause for a moment and think about it.

Assuming Ben is rational, the best answer is N, he will not wash the dishes. Why? Because whatever Jack chooses to do, Ben’s payoff in choosing N is always greater than his payoff in choosing Y. If Jack chooses Y, Ben’s choosing N will have a payoff of 3 while his choosing Y will only have a payoff of 2. If Jack chooses N, Ben’s choosing N will have a payoff of 1 while his choosing Y will only have a payoff of 0.

Hence, N strictly dominates strategy Y. But assuming Jack is also rational and utility-maximizing, he will also choose N, so that the outcome is (N,N) and they both get 1, which is Pareto inefficient.

Lesson: rational choices can lead to bad outcomes.

This example constitutes what is called the prisoner’s dilemma in the Game Theory of applied mathematics. Game Theory is a study of strategic situations. Strategic situations are situations where a person’s success in making choices depends on the choices of others.