Question

There are two players, governments of the developed world (i.e. US, EU, Japan, etc.) and governments of developing world (i.e. China, India, Brazil, etc.). An investment of $2 trillion is needed to stop global warming. It will produce economic benefits of $4 trillion, which will be split equally between the players. If the investment is not made, there will be economic losses of $4 trillion, which will be split equally between the players. If both parties agree to contribute, each need only invest $1 trillion. If only one party contributes, it must invest $2 trillion

a.Construct the game matrix of above situation. What is the equilibrium?

b.Is it possible to stop global warming, discuss briefly (i.e. discuss within the game theory context and develop a game by referring above payoffs?

Answer 1

A. The matrix for the game is presented in the figure above. It can be seen that when both type of nations invest, they both gain 2 trillion dollars but each spent 1 trillion each to gain it. Thus, each get net benefit of 1 trillion dollars.

Developing Nations Invest Not Invest invest (1,1) (0,2) Developed Nations Not invest (2,0) (-2,-2)

When only one type of country invests, the investing nations spend 2 trillion and also gain 2 trillion dollars worth benefits which makes their net benefit as zero. But the non-investing country gains 2 trillion dollars benefit without making any payment/investment.

When none of the two types of nations invest, both types of nations lose 2 trillion dollars each.

Now, we play the game using the matrix-

When developed nations choose to invest, the best decision for developing nations is to not invest (2 trillion>1 trillion).

When developed nations choose not to invest, the best decision for developing nations is to invest because payoff of 0 is better than -2 trillion.

Similarly, when developing nations choose to invest, the best decision for developed nations is to not invest (2 trillion payoff is better than 1 trillion).

When developing nations choose to not invest, the best decision for developed nations is to invest because 0 payoff is better than negative payoff.

Thus, this game has two nash equilibriums- (invest, not invest) and ( not invest, invest). Developing nations will invest if developed nations don't and vice-versa.

B. With this payoff matrix, it can be seen that nations will not be able to tackle global warming as each would wait for other to invest and gain a free rider benefit.

However if the payoff matrix is changed such that the investing nations gain more from their investment than the non-investing countries, the game's outcome would change. Suppose that if one type of nations invest, they would get all the benefits and other nations don't. Then game payoff will be like the following-

Now, for both the type of nations, dominant strategy is no invest in reducing global warming. The nash equilibrium will now be (invest, invest).

Developing Nations Invest Not Invest invest (1,1) (2,0) Developed Nations Not invest (0,2) (-2,-2)