9. Consider the following payoff matrix indicating payoffs from two countries (t
ID: 1132478 • Letter: 9
Question
9. Consider the following payoff matrix indicating payoffs from two countries (the U.S. and Canada) negotiating over reducing an air pollutant that crosses the boundaries of the two countries. Each has two strategies available to it: reduce the pollutant or not. The payoffs below are in millions.
a. Find the Nash equilibrium of this one-shot game. Be sure to identify any dominant strategy for either country. Is this a Prisoner's Dilemma?
b. Consider the payoffs to the U.S. when Canada reduces the pollutant, and the U.S. doesn’t reduce. Explain why the U.S. might receive a positive payoff when Canada reduces the pollutant but the U.S. doesn’t do anything?
Explanation / Answer
Answer:
a)
A Nash equilibrium is a point where either player has no incentive to deviate unilaterally from that point or else they will face a loss.
In this given game, the Nash equilibrium is "Don't reduce" and "Don't reduce". Both the countries in this game are not going to reduce any carbon emission. Starting from Japan's first move If Japan reduced and China didn't reduce its emission the Japan will face a loss of -3. And if the Chinese reduce but Japan didn't then the Chinese will face a loss of -3. If both cooperate and reduce the emissions they both get a return of 2 each but they have the incentive to deviate from that point and earn 5 instead of 2.
So, both the countries would choose the option of not reducing any emission and earn 0 instead of earning -3 (loss).
The dominant strategy for both the country is to don't reduce the emission no matter what the other country does. If the other reduced they benefit and get 5 and if they didn't they both are sitting pretty at 0 loss.
Yes, this is a prisoners dilemma.
b)
If he China alone reduces the emission and Japan doesn't then Japan's payoff is 5 because the reduction in emission is going to benefit both the countries but only China is taking initiative like using more renewable resources, less automobile etc which is harming its economy more. On the other hand, Japan can enjoy cleaner air to breathe, better climate etc without doing anything. Remember the Chinese are also enjoying these benefits of clean climate but they are paying for it and Japan is getting it for free. So their payoff is better.
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