Suppose two countries are engaged in the following pollution game. In the table below, the first number in each cell represents the payoff to country 1

Suppose two countries are engaged in the following pollution game. In the table below, the first number in each cell represents the payoff to country 1

Country 2

Pollute

Don’t pollute

Country 1

Pollute

2, 2

4, 1

Don’t pollute

1,4

3, 3

1) Suppose the countries play the game above for once. If each country 1 attempts to maximize its payoff, which action will each country choose?

2) Suppose the countries play the stage game given above repeatedly (for an indefinite number of times). Suppose each country applies (periodwise) discount rate r>0 to discount future payoffs. If a country receives payoffs X1, X2, X3, X4…, in periods 1, 2, 3, 4,…, then the present value of the payoffs would be

X1 + δ X2 + δ2 X3 + δ3 X4 +….

where δ = 1/(1+r).

Consider an international treaty for the two countries to choose “Don’t pollute” as long as both choose “Don’t pollute” in the previous period; and to choose “Pollute” if a country chooses “Pollute” in the previous period.

Suppose r = 0.05 (or 5%). Compare the net present value of abiding by the treaty (by choosing “Don’t pollute” in each period) and the net present value of deviating from the treaty (by choosing “Pollute” this period; and the remaining periods work as the treaty specifies). Do you expect the countries not to pollute under the treaty? Explain.

3) What if r = 1.5 (or 150%)? Do you expect the countries not to pollute under the treaty? Explain.

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