Classwork 12
International Climate Agreements
Consider two major economies, Country A and Country B, deciding whether to implement strict mitigation policies. Each country can choose to either “Reduce Emissions” or “Continue Business as Usual (BAU).” The payoff matrix below shows the economic benefits (in billions of dollars) for each country over a 10-year period.
| Country B | |||
|---|---|---|---|
| Reduce | BAU | ||
| Country A | Reduce | (5,5) | (-2,8) |
| BAU | (8,-2) | (1,1) | |
Question 1
What is the Nash equilibrium (or equilibria) in this game? Show your work.
We look for each country’s best response to the other country’s action.
Step 1: Best responses for Country A
- If Country B chooses “Reduce”:
- A’s payoff from Reduce = \(5\)
- A’s payoff from BAU = \(8\)
- Since \(8 > 5\), A prefers BAU.
- A’s payoff from Reduce = \(5\)
- If Country B chooses “BAU”:
- A’s payoff from Reduce = \(-2\)
- A’s payoff from BAU = \(1\)
- Since \(1 > -2\), A again prefers BAU.
- A’s payoff from Reduce = \(-2\)
Conclusion for A:
No matter what B does, A’s best response is BAU.
👉 BAU is a dominant strategy for Country A.
Step 2: Best responses for Country B
- If Country A chooses “Reduce”:
- B’s payoff from Reduce = \(5\)
- B’s payoff from BAU = \(8\)
- Since \(8 > 5\), B prefers BAU.
- B’s payoff from Reduce = \(5\)
- If Country A chooses “BAU”:
- B’s payoff from Reduce = \(-2\)
- B’s payoff from BAU = \(1\)
- Since \(1 > -2\), B again prefers BAU.
- B’s payoff from Reduce = \(-2\)
Conclusion for B:
No matter what A does, B’s best response is BAU.
👉 BAU is a dominant strategy for Country B.
Step 3: Nash equilibrium
A Nash equilibrium occurs where each country is playing a best response to the other.
- A’s dominant strategy → BAU
- B’s dominant strategy → BAU
So the strategy profile (BAU, BAU) is a Nash equilibrium, with payoffs:
\[ (\pi_A, \pi_B) = (1, 1) \]
There is no other Nash equilibrium because any outcome with at least one country choosing “Reduce” gives that country an incentive to deviate to BAU and increase its payoff.
Therefore, the unique Nash equilibrium is (BAU, BAU) with payoff \((1, 1)\).
Question 2
Explain why this game represents a Prisoner’s Dilemma in the context of climate change policy.
This game has the three key features of a classic Prisoner’s Dilemma:
- Individual dominant strategies lead to mutual defection
- For each country individually, choosing BAU yields a higher payoff regardless of what the other country does:
- If the other reduces, you get \(8\) (instead of \(5\)) by doing BAU.
- If the other does BAU, you get \(1\) (instead of \(-2\)) by doing BAU.
- So BAU is a dominant strategy for both A and B.
- For each country individually, choosing BAU yields a higher payoff regardless of what the other country does:
- Mutual defection is worse than mutual cooperation
- If both cooperate \((\text{Reduce}, \text{Reduce}) \Rightarrow\) payoffs \(= (5, 5)\)
- If both defect \((\text{BAU}, \text{BAU}) \Rightarrow\) payoffs \(= (1, 1)\)
- Each country would be better off in the cooperative outcome (since \(5 > 1\)), but they still end up in \((\text{BAU}, \text{BAU})\) when they act in their own narrow self-interest.
- Conflict between individual rationality and collective welfare
- From a global perspective, \((\text{Reduce}, \text{Reduce})\) is clearly better: higher total payoff and lower climate damages.
- From the perspective of each individual country, there is a strong incentive to free-ride:
- Enjoy the global climate benefits created by the other country’s mitigation while avoiding domestic mitigation costs.
In the climate policy context:
This captures the real-world problem that even though global cooperation on climate (strong mitigation by all) is collectively optimal, each country has a temptation to under-mitigate and free-ride on others’ efforts. Hence, the game is a Prisoner’s Dilemma applied to climate change.
Question 3
If the payoffs represent only economic benefits and ignore environmental costs:
Part A
What would be the socially optimal outcome?
To find the socially optimal outcome, we maximize the sum of payoffs to both countries:
- \((\text{Reduce}, \text{Reduce})\): total \(= 5 + 5 = 10\)
- \((\text{Reduce}, \text{BAU})\): total \(= -2 + 8 = 6\)
- \((\text{BAU}, \text{Reduce})\): total \(= 8 + (-2) = 6\)
- \((\text{BAU}, \text{BAU})\): total \(= 1 + 1 = 2\)
The largest total payoff is \(10\), which occurs under \((\text{Reduce}, \text{Reduce})\).
So, even ignoring environmental damages, the outcome where both countries reduce emissions already maximizes joint economic benefits in this stylized model.
If we then add environmental benefits (avoided climate damages, improved health, reduced disaster risk), \((\text{Reduce}, \text{Reduce})\) becomes even more strongly socially optimal.
Therefore, the socially optimal outcome is \((\text{Reduce}, \text{Reduce})\).
Part B
Why do countries tend to deviate from this outcome?
Even though \((\text{Reduce}, \text{Reduce})\) is socially optimal, countries may deviate because of several incentives and constraints:
- Free-rider problem
- Climate mitigation is a global public good: one country’s emission cuts benefit everyone.
- Each country is tempted to enjoy the benefits of others’ reductions while avoiding its own costs.
- This creates a strong incentive to choose BAU while hoping others will reduce.
- Short-term vs. long-term trade-offs
- Mitigation often involves upfront costs (e.g., clean energy investment, phasing out coal).
- Political leaders may prioritize short-term GDP growth, jobs, and re-election over long-term climate benefits.
- This short-run bias makes BAU politically attractive, even if worse in the long run.
- Lack of enforcement mechanisms
- There is no global government to impose binding penalties for non-compliance.
- International climate agreements rely on voluntary pledges and peer pressure, which may be insufficient to sustain cooperation.
- Distributional and fairness concerns
- Countries may feel climate responsibilities are unequally shared (e.g., historical emitters vs. developing nations).
- Perceived unfairness weakens willingness to cooperate, making unilateral BAU more politically acceptable.
Because of these forces, countries often behave according to individual rationality (choosing BAU) rather than collective rationality (mutual reduction).
Question 4
Consider implementing a policy mechanism to modify the payoff structure of this climate agreement game.
Part A
Suggest and explain a specific policy mechanism (e.g., carbon border adjustments, trade sanctions, or technology subsidies) that could alter the payoffs.
CBAM
One concrete mechanism is a Carbon Border Adjustment Mechanism (CBAM) combined with climate penalties for persistent BAU:
- Basic idea:
- Countries that Reduce emissions can impose a carbon tariff on imports from countries that remain in BAU.
- Revenue from this tariff can be partly used to compensate reducing countries for their mitigation costs.
- If both stay in BAU, they face higher climate-related damages (e.g., storms, heat waves, sea-level rise) and possibly coordinated sanctions from a “climate club.”
- Effects on payoffs:
- A country that chooses BAU while its partner reduces:
- Loses market access and faces border tariffs, lowering its net economic gains.
- Faces reputational and diplomatic costs (reduced cooperation in other policy areas).
- A country that chooses Reduce while its partner stays in BAU:
- Receives tariff revenue transfers, helping to offset mitigation costs.
- Suffers less from carbon leakage, because high-emission imports are taxed.
- If both stay in BAU:
- There are no tariff revenues, but both suffer larger climate damages and may face joint sanctions from a climate club.
- A country that chooses BAU while its partner reduces:
By designing the CBAM and penalty structure appropriately, we can raise the cost of BAU and reduce the cost of reducing, so that \((\text{Reduce}, \text{Reduce})\) becomes individually rational as well as socially optimal.
Climate Club
Another powerful mechanism is forming an International Climate Club that uses coordinated incentives and penalties to shift countries toward cooperation:
- Basic idea of a Climate Club:
- A group of countries commits to strong emission reductions and agrees on a minimum carbon price (e.g., $75/ton).
- Club members grant mutual benefits to each other—such as free trade in low-carbon products, technology sharing, or clean-energy investment financing.
- Non-members face common external tariffs on carbon-intensive goods when exporting to club members.
- Effects on incentives:
- Joining the club becomes beneficial because members enjoy:
- Preferential market access
- Lower trade barriers
- Access to shared clean-tech innovation
- Financial and technical support for decarbonization
- Preferential market access
- Staying outside the club becomes costly because:
- Non-members face uniform tariffs on exports to all club members.
- They risk losing competitiveness in global markets.
- They receive no access to green financing or technology pools.
- They suffer larger climate damages as decarbonization is delayed.
- Joining the club becomes beneficial because members enjoy:
- Why it changes payoffs:
- A country choosing BAU while others reduce:
- Pays external club tariffs, making BAU significantly less profitable.
- Loses access to club benefits, technology, and markets.
- A country choosing Reduce:
- Gains entry into the club and enjoys higher net economic returns through trade advantages and coordinated investments.
- If both countries stay in BAU:
- Both remain outside the club and face greater climate damages and loss of competitiveness.
- A country choosing BAU while others reduce:
By establishing a Climate Club with shared standards and unified penalties, the international community can reshape incentives so that global cooperation—\((\text{Reduce}, \text{Reduce})\)—becomes attractive and individually rational, rather than relying on voluntary goodwill alone.
Part B
Provide a new payoff matrix that incorporates your suggested policy mechanism. Show all calculations for the modified payoffs.
New Payoff Matrix with Policy
| Country B | |||
|---|---|---|---|
| Reduce | BAU | ||
| Country A | Reduce | (5,5) | (0,4) |
| BAU | (4,0) | (-3,-3) | |
We start from the original payoffs and then adjust them to reflect:
- Tariffs and penalties on BAU when the other country reduces.
- Additional climate damages / sanctions when both stay in BAU.
- Compensation to reducers via tariff revenues.
Step 1: Original payoff matrix (for reference)
- \((\text{Reduce}, \text{Reduce}): (5, 5)\)
- \((\text{Reduce}, \text{BAU}): (-2, 8)\)
- \((\text{BAU}, \text{Reduce}): (8, -2)\)
- \((\text{BAU}, \text{BAU}): (1, 1)\)
Step 2: Introduce CBAM and penalties
1. Case \((\text{Reduce}, \text{Reduce})\)
- Both countries reduce, so no CBAM applies.
- Cooperative outcome remains unchanged:
\[ (5, 5) \quad \text{(no change)} \]
2. Case \((\text{Reduce}, \text{BAU})\) — A reduces, B remains BAU
- Country B faces a carbon border tariff + penalties equivalent to \(4\) units:
- B’s payoff: \(8 - 4 = 4\)
- Part of tariff revenue (\(2\) units) is transferred to A to help offset mitigation costs:
- A’s payoff: \(-2 + 2 = 0\)
- Remaining \(2\) units may go to administrative or global climate funds.
New payoffs:
\[ (\text{Reduce}, \text{BAU}) : (0, 4) \]
3. Case \((\text{BAU}, \text{Reduce})\) — A is BAU, B reduces
By symmetry:
- A (BAU) pays \(4\) in penalties: \(8 - 4 = 4\)
- B (Reduce) receives \(2\) in compensation: \(-2 + 2 = 0\)
New payoffs:
\[ (\text{BAU}, \text{Reduce}) : (4, 0) \]
4. Case \((\text{BAU}, \text{BAU})\) — both stay in BAU
No tariff revenue.
Both face higher climate damages and potential climate-club sanctions.
Total costs reduce each payoff by \(4\):
A: \(1 - 4 = -3\)
B: \(1 - 4 = -3\)
New payoffs:
\[ (\text{BAU}, \text{BAU}) : (-3, -3) \]
Part C
Prove that under your proposed policy:
- The socially optimal outcome (Reduce, Reduce) becomes a Nash equilibrium
Show answer
We now analyze best responses using the modified payoff matrix.
Step 1: Best responses for Country A
- If B chooses “Reduce”:
- A’s payoff from Reduce = \(5\)
- A’s payoff from BAU = \(4\)
- Since \(5 > 4\), A’s best response is Reduce.
- A’s payoff from Reduce = \(5\)
- If B chooses “BAU”:
- A’s payoff from Reduce = \(0\)
- A’s payoff from BAU = \(-3\)
- Since \(0 > -3\), A’s best response is again Reduce.
- A’s payoff from Reduce = \(0\)
👉 Reduce is now a dominant strategy for Country A.
Step 2: Best responses for Country B
By symmetry:
- If A chooses “Reduce”:
- B’s payoff from Reduce = \(5\)
- B’s payoff from BAU = \(4\)
- Best response: Reduce.
- B’s payoff from Reduce = \(5\)
- If A chooses “BAU”:
- B’s payoff from Reduce = \(0\)
- B’s payoff from BAU = \(-3\)
- Best response: Reduce.
- B’s payoff from Reduce = \(0\)
👉 Reduce is also a dominant strategy for Country B.
Conclusion
The policy (CBAM + penalties) changes the incentive structure so that the socially optimal cooperative outcome \((\text{Reduce}, \text{Reduce})\) is also a Nash equilibrium.
Individual rationality and collective welfare are now aligned.
Part D
Discuss one potential challenge in implementing your proposed policy mechanism in the real world.
A major challenge is designing and enforcing the climate club and its penalty system in a politically and legally feasible way:
- Political resistance and trade tensions
- Countries targeted by club tariffs or exclusion measures may view them as disguised protectionism rather than legitimate climate policy.
- This can trigger retaliatory tariffs, trade disputes, and undermine international cooperation.
- Governments face strong domestic lobbying from carbon-intensive industries that fear losing competitiveness.
- Measurement and verification problems
- Fair implementation requires reliable, comparable data on the carbon content of goods and production processes.
- Many countries lack robust MRV (Measurement, Reporting, and Verification) systems.
- Disagreements about data, methodologies, and baselines can erode trust and delay enforcement.
- Legal constraints (e.g., WTO rules)
- Climate clubs often rely on common external tariffs or preferential treatment for members—actions that may conflict with WTO non-discrimination principles (Most-Favored Nation and National Treatment).
- Unless carefully designed, a climate club could be viewed as violating WTO rules, especially if penalties discriminate between members and non-members.
- If challenged successfully at the WTO, the mechanism might be weakened, forced to change, or suspended.
Even though the theoretical incentive structure of a climate club can make Reduce a dominant strategy, these practical political and legal barriers can limit the club’s effectiveness or prevent full implementation in real-world climate governance.