Consider the case of global environmental problems that spill across international borders as a prisoner’s dilemma of the sort studied in Monopolistic Competition and Oligopoly. Say that there are two countries, A and B. Each country can choose whether to protect the environment, at a cost of 10, or not to protect it, at a cost of zero. If one country decides to protect the environment, there is a benefit of 16, but the benefit is divided equally between the two countries. If both countries decide to protect the environment, there is a benefit of 32, which is divided equally between the two countries.

Begin by organizing the information given in the exercise as a matrix that represents the payoff for each country based on their choices. This matrix is known as a "payoff matrix." Here, the first number in each cell represents the payoff for Country A, and the second number represents the payoff for Country B. | Country B | Protect | Not Protect -------|---------|------------ Protect | (16, 16) | (8, 6) Country A Not Protect | (6, 8) | (0, 0)

List all the possible outcomes based on the decisions of countries A and B: 1. Both countries protect the environment. 2. Both countries do not protect the environment. 3. Country A protects the environment, but Country B does not. 4. Country A does not protect the environment, and Country B does.

Compute the payoffs for each country under each possible outcome: 1. Both countries protect the environment: They both pay a cost of 10 but receive a benefit of 32 (divided equally). So, the payoff is (16-10, 16-10) = (6,6). 2. Both countries do not protect the environment: They save the cost of 10 but also don't receive any benefit. So, the payoff is (0,0). 3. Country A protects the environment, Country B does not: Country A pays the cost of 10, and the total benefit is 16 (divided equally). So, the payoff is (8-10, 8) = (-2,8). 4. Country A does not protect the environment, Country B does: Country B pays the cost of 10 and the total benefit is 16 (divided equally). So, the payoff is (8, 8-10) = (8,-2). Now, update the payoff matrix with these calculated payoffs: | Country B | Protect | Not Protect -------|---------|------------ Protect | (6, 6) | (-2, 8) Country A Not Protect | (8, -2) | (0, 0)

A Nash equilibrium is a decision-making situation in which each country is choosing their best response, given the strategy of the other country. No one has an incentive to deviate from their strategy, knowing that the other country is also choosing their best response. In the payoff matrix, identify the best response for: - Country A (row player): - If Country B chooses Protect: Country A earns 6 when protecting and 8 when not. So the best response is Not Protect. - If Country B chooses Not Protect: Country A earns -2 when protecting and 0 when not. So the best response is Not Protect. - Country B (column player): - If Country A chooses Protect: Country B earns 6 when protecting and 8 when not. So the best response is Not Protect. - If Country A chooses Not Protect: Country B earns -2 when protecting and 0 when not. So the best response is Not Protect. Since both Country A and Country B have a best response of choosing "Not Protect," the Nash equilibrium occurs when both countries choose "Not Protect," with the resulting payoff being (0, 0). So, in this prisoner's dilemma-type scenario, the best strategy for both countries is not to protect the environment, which may lead to suboptimal solutions for the global environmental problem.