9. (8 points) ) Consider the following payoff matrix indicating payoffs from two
ID: 1121434 • Letter: 9
Question
9. (8 points) ) Consider the following payoff matrix indicating payoffs from two countries (Japan and China) negotiating over reducing carbon emissions. Each has two strategies available to it: reduce carbon emissions or not. The payoff for each country is given in the table as (Payoff for Japan, Payoff for China) China Don't reduce Reduce Don't reduce 0, O 5, -3 Japan Reduce 3, 5 2, 2 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 Japan when China reduces emissions, and Japan doesn't reduce. Explain why Japan might receive a positive payoff whern China reduces the pollutant but Japan doesn't do anything? c. Using the game above, describe a tax mechanism and solve for the tax level that would generate a Nash Equilibrium in which both countries reduce carbon emissionS.Explanation / 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.
c) We can set up a tax regime which charges the country for not introducing any reduction in carbon emission. In such a case if the country didn't reduce its emission they have to pay taxes i.e. face losses. The tax should be at least "5". So if the country didn't reduce its emission they face a loss of 5, but if they do even unilaterally they have a loss of only 3 which is less than 5. In that scenario, both will work for the reduction of emission and get a benefit of 2 each.
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