The problem of climate change will require global cooperation. Imagine there are three countries in the global economy of the same size. Each country...

The problem of climate change will require global cooperation. Imagine there are three countries in the global economy of the same size. Each country emits 4 gigatons of CO2 each year. Reducing 1 gigaton of emissions will cost each country $30 billion. However, each gigaton of reduced emission will provide $60 billion in benefits divided among the 3 countries of the world proportional to population. The 3 countries' populations are initially equal. The benefits stem from reduced damages due to disasters and temperature changes (these numbers are approximately accurate incidentally).

1. (a) What is the payoff for each player as a function of the strategy profiles?
2. (b) Calculate the welfare maximizing choice of emission levels.
3. (c) Compute the set of rationalizable emissions levels for each player.
4. (d) Suppose one country conquers another country. Now there are two countries, one with 1/3 of global population responsible for 4 gigatons, the other with 2/3 of global population responsible for 8 gigatons. It still costs each country the same amount per gigaton to reduce emissions. Compute the set of rationalizable effort levels.
5. (e) Suppose the world enters an age of enlightenment. The conquering country lets the conquered country go so that we are now back to the world with three equal sized countries. In the spirit of altruism, countries now maximize their own payoffs plus β times the total welfare of the world. How high does β have to be to achieve the welfare maximizing choice of emission levels.