Question

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. a. In Table 12.10 , fill in the costs, benefits, and total payoffs to the countries of the following decisions. Explain why, without some international agreement, they are likely to end up with neither country acting to protect the environment.

Short answer

In the prisoner's dilemma of global environmental problems, the Nash equilibrium leads to neither country A nor country B protecting the environment, as it is each country's best individual response considering the other's choice. However, both countries would be better off if they both chose to protect the environment. This highlights the need for international agreements to encourage cooperation and achieve greater environmental benefits for all involved.

Step-by-step solution

Create a Payoff Table

Before analyzing the outcomes and finding the Nash equilibrium, let's create a table representing the payoffs for each possible decision made by Country A and Country B. We will use the following notation: (A's Payoff, B's Payoff). Decision Combinations | Country A Protects | Country A Doesn't Protect ----------------------------------|-----------------------|-------------------------- Country B Protects | (A , B) | (A , B) Country B Doesn't Protect | (A , B) | (A , B)

Fill in the Payoffs

Now, let's fill in the table with the given costs and benefits: 1. If both countries protect the environment, the total benefit is \(32\), and each country gets an equal share of \(16\). Each country has a cost of \(10\), so the payoff for each country is \(16 - 10 = 6\). The table will look like this: Decision Combinations | Country A Protects | Country A Doesn't Protect ----------------------------------|-----------------------|-------------------------- Country B Protects | (6 , 6) | (A , B) Country B Doesn't Protect | (A , B) | (A , B) 2. If Country A protects while Country B doesn't, the total benefit is \(16\), and each country gets an equal share of \(8\). Country A has a cost of \(10\), so its payoff is \(8 - 10 = -2\). But Country B has no cost, so its payoff is \(8\). The table will look like this: Decision Combinations | Country A Protects | Country A Doesn't Protect ----------------------------------|-----------------------|-------------------------- Country B Protects | (6 , 6) | (A , B) Country B Doesn't Protect | (-2 , 8) | (A , B) 3. If Country A doesn't protect while Country B does, we have the same situation as in step 2 but with reversed roles. So, Country A's payoff is 8 and Country B's payoff is -2. The table will look like this: Decision Combinations | Country A Protects | Country A Doesn't Protect ----------------------------------|-----------------------|-------------------------- Country B Protects | (6 , 6) | (-2 , 8) Country B Doesn't Protect | (-2 , 8) | (A , B) 4. If neither country protects, there is no benefit and also no cost. So, the payoff for both countries is 0. The table will look like this: Decision Combinations | Country A Protects | Country A Doesn't Protect ----------------------------------|-----------------------|-------------------------- Country B Protects | (6 , 6) | (-2 , 8) Country B Doesn't Protect | (-2 , 8) | (0 , 0)

Analyze the Nash Equilibrium

Now, let's find the Nash equilibrium by analyzing each country's best response when considering the other country's decision. 1. If Country B protects, Country A's payoffs are 6 when protecting and -2 when not protecting. Country A is better off protecting as well. 2. If Country B doesn't protect, Country A's payoffs are -2 when protecting and 0 when not protecting. Country A is better off not protecting. 3. If Country A protects, Country B's payoffs are 6 when protecting and 8 when not protecting. Country B is better off not protecting. 4. If Country A doesn't protect, Country B's payoffs are -2 when protecting and 0 when not protecting. Country B is better off not protecting. The Nash equilibrium occurs when neither country protects the environment. This is because both countries will choose not to protect, given the decision of the other country.

Conclusion

In this problem, there is a prisoner's dilemma situation, where the Nash equilibrium (without international agreements) results in neither country acting to protect the environment, even though both countries would be better off if they both choose to protect the environment. An international agreement can be helpful in achieving cooperation and incentivizing both countries to protect the environment in order to achieve greater benefits.

Key concepts

International Agreements

International agreements play a critical role in addressing global challenges such as environmental protection. Without these agreements, countries may not find it beneficial to act individually due to disincentives highlighted in scenarios like the prisoner's dilemma.

• International agreements provide a framework for cooperation, encouraging countries to take collective action that leads to better outcomes.
• They help establish rules, standards, and guidelines that ensure countries work towards common goals. This can include commitments to reduce emissions or protect biodiversity.
• These agreements can also offer supportive mechanisms, such as financial aid or technology sharing, to mitigate costs for participating countries.

By formalizing commitments, international agreements can move countries away from suboptimal outcomes (like the Nash equilibrium in the prisoner's dilemma) and towards mutually beneficial actions.

Game Theory

Game theory is a mathematical framework used to understand strategic interactions between decision-makers. In the context of the prisoner's dilemma, which is a classical model in game theory, it explains why countries may fail to cooperate, even when it seems mutually beneficial to do so.

• The prisoner's dilemma illustrates a situation where individual decision-makers, acting in their own self-interest, lead to a worse outcome collectively.
• Game theory helps us predict behavior based on the payoffs of different choices and the likelihood that others will cooperate or defect.
• This framework is applicable beyond international relations, influencing economics, business strategy, and beyond.

Understanding these dynamics allows us to design strategies, such as international treaties, that redefine the payoffs and promote cooperative behavior.

Environmental Economics

Environmental economics focuses on the economic impacts of environmental policies and the costs and benefits associated with environmental protection. It extends the discussion of the prisoner's dilemma to real-world policy-making.

• This field assesses how resources can be managed sustainably and how environmental damage can be mitigated through economic incentives.
• It involves tools like cost-benefit analysis to evaluate the net benefits of environmental protection measures.
• Environmental economics also explores market-based solutions, such as carbon pricing or tradable permits, designed to encourage environmental stewardship.

Through economic analysis, it becomes clearer how policies can be structured to achieve better environmental outcomes and overcome challenges highlighted in the prisoner's dilemma.

Nash Equilibrium

The Nash equilibrium in the context of the prisoner's dilemma provides insight into why rational players might choose suboptimal strategies. In the exercise concerning environmental protection, it highlights a crucial point of mutual non-cooperation.

• Nash equilibrium occurs when no player can benefit by changing their strategy while the other players keep theirs unchanged.
• In the example, both countries choose not to protect the environment, resulting in a zero payoff, because unilateral action doesn't yield a net benefit given the cost of protection.
• This explains why, without intervention, countries stick to the "safe" strategy of doing nothing, despite the higher collective benefit available through cooperation.

Understanding Nash equilibrium encourages the search for mechanisms, like international agreements, that alter incentives and break the cycle of non-cooperation.