2. Ten countries are considering fighting global warming by entering into an agreement. Under the agreement, a country must decide to spend an amount x; to reduce its carbon emission, where 0 x S1. Note that the subscript represents the ith, country and i ranges from 1to 10. The total benefits B produced under this agreement is twice the sum total of the spending made by all 10 countries. Each country receives a benefit which is one-tenth of the total benefit B. The payoff of any country is the net benefit, ie., the benefit that it receives less its own spending. (a) Write an equation for the payoff of any country. (b) Using the payoff function of (a) prove that spending nothing (x = 0) is the dominant strategy for any country. (c) Calculate the payoff of each country if they could somehow agree to spend 1 each. (d) Based on your answers to (b) and (c) how can you characterize this game, i.e., what type of game is this?